Samacheer Kalvi solutions for Mathematics [English] Class 8 TN Board chapter 3 - Algebra [Latest edition]

Complete the table.

Find the product of the terms

−2mn, (2m)², −3mn

Find the product of the terms

3x²y , −3xy³, x²y²

If l = 4pq², b = −3p²q, h = 2p³q³ then, find the value of l × b × h

Expand 5x(2y – 3)

Expand −2p(5p² – 3p + 7)

Expand 3mn(m³n³ – 5m²n + 7mn²)

Expand x²(x + y + z) + y²(x + y + z) + z²(x – y – z)

Find the product of (2x + 3)(2x – 4)

Find the product of (y² – 4)(2y² + 3y)

Find the product of (m² – n)(5m²n² – n²)

Find the product of 3(x – 5) × 2(x – 1)

Find the missing term

6xy × _________ = –12x³y

Find the missing term

_________ × (−15m²n³p) = 45m³n³p²

Find the missing term

2y(5x²y – ___ + 3 ___ ) = 10x²y² – 2xy + 6y³

Match the following:

A car moves at a uniform speed of (x + 30) km/hr. Find the distance covered by the car in (y + 2)hours. (Hint: distance = speed × time).

The product of 7p³ and (2p²)² is

The missing terms in the product −3m³n × 9(__) = _________ m⁴n³

If the area of a square is 36x⁴y² then, its side is ____________

If the area of a rectangle is 48m²n³ and whose length is 8mn² then, its breadth is _______

If the area of a rectangular land is (a² – b²) sq.units whose breadth is (a – b) then, its length is __________

`(18"m"^4(_))/(2"m"^3"n"^3` = _____ mn⁵ 

`("l"^4"m"^5"n"^((_)))/(2"l""m"^((_))"n"^6) = ("l"^3"m"^3"n")/((_))`

`(42"a"^4"b"^5(_))/(6"a"^4"b"^2)` = `(_)"b"^((_))"c"^2`

8x³y ÷ 4x² = 2xy

7ab³ ÷ 14ab = 2b²

Divide 27y³ by 3y

Divide x³y² by x²y

Divide 45x³y²z⁴ by (−15xyz)

Divide (3xy)² by 9xy

Simplify `(3"m"^2)/"m" + (2"m"^4)/("m"^3)`

Simplify `(14"p"^5"q"^3)/(2"p"^2"q") - (12"p"^3"q"^4)/(3"q"^2)`

Divide: (32y² – 8yz) by 2y

Divide: (4m²n³ + 16m⁴n² – mn) by 2mn

Divide:

5xy² – 18x²y³ + 6xy by 6xy

Divide: 81(p⁴q²r³ + 2p³q³r² – 5p²q²r²) by (3pqr)²

Identify the errors and correct them

7y² – y² + 3y² = 10y² 

Identify the errors and correct them

6xy + 3xy = 9x²y² 

Identify the errors and correct them

m(4m – 3) = 4m² – 3

Identify the errors and correct them

(4n)² – 2n + 3 = 4n² – 2n + 3

Identify the errors and correct them

(x – 2)(x + 3) = x² – 6

Identify the errors and correct them

– 3p² + 4p – 7 = – (3p² + 4p – 7)

Statement A: If 24p²q is divided by 3pq, then the quotient is 8p.

Statement B: Simplification of `((5x + 5))/5` is 5x

Statement A: 4x² + 3x – 2 = `2(2x^2 + (3x)/2 - 1)`

Statement B: (2m – 5) – (5 – 2m) = (2m – 5) + (2m – 5)

Expand (3m + 5)²

Expand (5p – 1)²

Expand (2n – 1)(2n + 3)

Expand 4p² – 25q²

Expand (3 + m)³ 

Expand (2a + 5)³ 

Expand (3p + 4q)³

Expand (52)³

Expand (104)³

Expand (5 − x)³

Expand (2x – 4y)³

Expand (ab – c)³

Expand (48)³

Expand (97xy)³

Simplify (p – 2)(p + 1)(p – 4)

Find the volume of the cube whose side is (x + 1) cm

Find the volume of the cuboid whose dimensions are (x + 2), (x – 1) and (x – 3)

If x² – y² = 16 and (x + y) = 8 then (x – y) is ___________

`(("a" + "b")("a"^3 - "b"^3))/(("a"^2 - "b"^2))` = ___________

(p + q)(p² – pq + q²) is equal to _____________

(a – b) = 3 and ab = 5 then a³ – b³ = __________

a³ + b³ = (a + b)³ = __________

Factorise the following by taking out the common factor

18xy – 12yz

Factorise the following by taking out the common factor

9x⁵y³ + 6x³y² – 18x²y

Factorise the following by taking out the common factor

x(b – 2c) + y(b – 2c)

Factorise the following by taking out the common factor

(ax + ay) + (bx + by)

Factorise the following by taking out the common factor

2x²(4x – 1) – 4x + 1

Factorise the following by taking out the common factor

3y(x – 2)² – 2(2 – x)

Factorise the following by taking out the common factor

6xy – 4y² + 12xy – 2yzx

Factorise the following by taking out the common factor

a³ – 3a² + a – 3

Factorise the following by taking out the common factor

3y³ – 48y

Factorise the following by taking out the common factor

ab² – bc² – ab + c²

Factorise the following expressions

x² + 14x + 49

Factorise the following expressions

y² – 10y + 25

Factorise the following expressions

c² – 4c – 12

Factorise the following expressions

m² + m – 72

Factorise the following expressions

4x² – 8x + 3

Factorise the following expressions using (a + b)³ = a³ + 3a²b + 3ab² + b³ identity 

64x³ + 144x² + 108x + 27

Factorise the following expressions using (a + b)³ = a³ + 3a²b + 3ab² + b³ identity 

27p³ + 54p²q + 36pq² + 8q³

Factorise the following expressions using (a – b)³ = a³ – 3a²b + 3ab² – b³ identity

y³ – 18y² + 108y – 216

Factorise the following expressions using (a – b)³ = a³ – 3a²b + 3ab² – b³ identity

8m³ – 60m²n + 150mn² – 125n³

Factors of 9x² + 6xy are

Factors of 4 – m² are

(x + 4) and (x – 5) are the factors of ___________

The factors of x² – 5x + 6 are (x – 2)(x – p) then the value of p is ______.

The factors of 1 – m³ 

One factor of x³ + y³ is

Subtract: −2(xy)² (y³ + 7x²y + 5) from 5y² (x²y³ – 2x⁴y + 10x²)

Multiply (4x² + 9) and (3x – 2)

Find the simple interest on Rs. 5a²b² for 4ab years at 7b% per annum

The cost of a notebook is Rs. 10ab. If Babu has Rs. (5a²b + 20ab² + 40ab). Then how many notebooks can he buy?

Factorise: (7y² – 19y – 6)

A contractor uses the expression 4x² + 11x + 6 to determine the amount of wire to order when wiring a house. If the expression comes from multiplying the number of rooms times the number of outlets and he knows the number of rooms to be (x + 2), find the number of outlets in terms of ’x’. [Hint : factorise 4x² + 11x + 6]

A mason uses the expression x² + 6x + 8 to represent the area of the floor of a room. If the decides that the length of the room will be represented by (x + 4), what will the width of the room be in terms of x?

Find the missing term: y² + (...)x + 56 = (y + 7)(y + ...)

Factorise : 16p⁴ – 1

Factorise : 3x³ – 45x²y + 225xy² – 375y³

The value of x in the equation x + 5 = 12 is _________

The value of y in the equation y – 9 = (– 5) + 7 is ________

The value of m in the equation 8m = 56 is ________

The value of p in the equation `(2"p")/3` = 10 is ________

The linear equation in one variable has ________ solution

The shifting of a number from one side of an equation to other is called transposition

Linear equation in one variable has only one variable with power 2

Match the following :

Find x and p: `(2x)/3 - 4 = 10/3`

Find x and p: `y + 1/6 - 3y = 2/3`

Find x and p: `1/3 - x/3 = (7x)/12 + 5/4`

Find x: −3(4x + 9) = 21

Find x: 20 – 2(5 – p) = 8

Find x: (7x – 5) – 4(2 + 5x) = 10(2 – x)

Find x and m: `(3x - 2)/4 - ((x - 3))/5` = −1

Find x and m: `("m" + 9)/(3"m" + 15) = 5/3`

The solution of the equation ax + b = 0 is _______

If a and b are positive integers then the solution of the equation ax = b has to be always _______

One-sixth of a number when subtracted from the number itself gives 25. The number is _______

If the angles of a triangle are in the ratio 2 : 3 : 4 then the difference between the greatest and the smallest angle is _______

In an equation a + b = 23. The value of a is 14 then the value of b is _______

“Sum of a number and two times that number is 48” can be written as y + 2y = 48

5(3x + 2) = 3(5x – 7) is a linear equation in one variable

x = 25 is the solution of one third of a number is less than 10 the original number.

One number is seven times another. If their difference is 18, find the numbers

The sum of three consecutive odd numbers is 75. Which is the largest among them?

The length of a rectangle is `1/3` of its breadth. If its perimeter is 64 m, then find the length and breadth of the rectangle.

A total of 90 currency notes, consisting only of ₹ 5 and ₹ 10 denominations, amount to ₹ 500. Find the number of notes in each denomination.

At present, Thenmozhi’s age is 5 years more than that of Murali’s age. Five years ago, the ratio of Thenmozhi’s age to Murali’s age was 3 : 2. Find their present ages.

A number consists of two digits whose sum is 9. If 27 is subtracted from the original number, its digits are interchanged. Find the original number

The denominator of a fraction exceeds Its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, we get `3/2`. Find the original fraction.

If a train runs at 60 km/hr it reaches its destination late by 15 minutes. But, if it runs at 85 kmph it is late by only 4 minutes. Find the distance to be covered by the train.

Sum of a number and its half is 30 then the number is ______ 

The exterior angle of a triangle is 120° and one of its interior opposite angle 58°, then the other opposite interior angle is _________

What sum of money will earn ₹ 500 as simple interest in 1 year at 5% per annum?

The product of L.C.M and H.C.F of two numbers is 24. If one of the number is 6, then the other number is ________

The largest number of the three consecutive numbers is x + 1, then the smallest number is ________

X-axis and Y-axis intersect at _________

The coordinates of the point in third quadrant are always _________ 

(0, −5) point lies on _________ axis

The x-coordinate is always ______ on the y-axis

___________ coordinates are the same for a line parallel to Y-axis

(−10, 20) lies in the second quadrant

(−9, 0) lies on the x-axis

The coordinates of the origin are (1, 1)

Find the quadrants without plotting the point on a graph sheet

(3, −4)

Find the quadrants without plotting the point on a graph sheet.

(5, 7)

Find the quadrants without plotting the point on a graph sheet.

(2, 0)

Find the quadrants without plotting the point on a graph sheet

(−3, −5)

Find the quadrants without plotting the point on a graph sheet

(4, −3)

Find the quadrants without plotting the point on a graph sheet

(−7, 2)

Find the quadrants without plotting the point on a graph sheet.

(−8, 0)

Find the quadrants without plotting the point on a graph sheet.

(0, 10)

Find the quadrants without plotting the point on a graph sheet.

(−9, 50)

Plot the following point in a graph sheet.

A(5, 2)

Plot the following point in a graph sheet.

B(−7, −3)

Plot the following point in a graph sheet.

C(−2, 4)

Plot the following point in a graph sheet.

D(−1, −1)

Plot the following point in a graph sheet.

E(0, −5)

Plot the following point in a graph sheet.

F(2, 0)

Plot the following point in a graph sheet.

G(7, −4)

Plot the following point in a graph sheet.

H(−4, 0)

Plot the following point in a graph sheet.

I(2, 3)

Plot the following point in a graph sheet.

J(8, −4)

Plot the following point in a graph sheet.

K(0, 7)

Use the graph to determine the coordinates where each figure is located.

y = px where p ∈ Z always passes through the _________

The intersecting point of the line x = 4 and y = −4 is _________

Scale for the given graph,

On the x-axis 1 cm = _________ units
y-axis 1 cm = _________ units

The points (1, 1) (2, 2) (3, 3) lie on a same straight line

y = −9x not passes through the origin

Will a line pass through (2, 2) if it intersects the axes at (2, 0) and (0, 2)

A line passing through (4, – 2) and intersects the Y-axis at (0, 2). Find a point on the line in the second quadrant

If the points P(5, 3) Q(−3, 3) R(−3, −4) and S form a rectangle then find the coordinate of S

A line passes through (6, 0) and (0, 6) and an another line passes through (−3, 0) and (0, −3). What are the points to be joined to get a trapezium?

Find the point of intersection of the line joining points (– 3, 7) (2, – 4) and (4, 6) (–5, – 7). Also, find the point of intersection of these lines and also their intersection with the axis.

Draw the graph of the following equation:

x = – 7

Draw the graph of the following equation:

y = 6

Draw the graph of y = – 3x

Draw the graph of y = x – 4

Draw the graph of y = 2x + 5

Find the values.
y = x + 3

Find the values.

2x + y − 6 = 0

Find the values.

y = 3x + 1

The sum of three numbers is 58. The second number is three times of two-fifth of the first number and the third number is 6 less than the first number. Find the three numbers

In triangle ABC, the measure of ∠B is two-third of the measure of ∠A. The measure of ∠C is 20° more than the measure of ∠A. Find the measures of the three angles.

Two equal sides of an isosceles triangle are 5y – 2 and 4y + 9 units. The third side is 2y + 5 units. Find ‘y’ and the perimeter of the triangle.

In the given figure, angle XOZ and angle ZOY form a linear pair. Find the value of x

Draw a graph for the following data:

Does the graph represent a linear relation?

Three consecutive integers, when taken in increasing order and multiplied by 2, 3 and 4 respectively, total up to 74. Find the three numbers.

331 students went on a field trip. Six buses were filled to capacity and 7 students had to travel in a van. How many students were there in each bus?

A mobile vendor has 22 items, some which are pencils and others are ball pens. On a particular day, he is able to sell the pencils and ball pens. Pencils are sold for ₹ 15 each and ball pens are sold at ₹ 20 each. If the total sale amount with the vendor is ₹ 380, how many pencils did he sell?

Draw the graph of the lines y = x, y = 2x, y = 3x and y = 5x on the same graph sheet. Is there anything special that you find in these graphs?

Consider the number of angles of a convex polygon and the number of sides of that polygon. Tabulate as follows:

Use this to draw a graph illustrating the relationship between the number of angles and the number of sides of a polygon