###### Advertisements

###### Advertisements

Factorize 8a^{3} – 27b^{3} – 36a^{2}b + 54ab^{2}

###### Advertisements

#### Solution

8a^{3} - 27b^{3} - 36a^{2}b + 54ab^{2}

= (2a)^{3} - (3b)^{3} - 3 × (2a)^{2} 3b + 3(2a)(3b)^{2}

= (2a - 3b)^{3} [∵ a^{3} - b^{3} - 3a^{2}b + 3ab^{2} = (a - b)^{3} ]

= (2a - 3b)(2a - 3b)(2a - 3b)

∴ 8a^{3} - 27b^{3} - 36a^{2}b + 54ab^{2} = (2a - 3b)(2a - 3b)(2a - 3b)

#### APPEARS IN

#### RELATED QUESTIONS

Get the algebraic expression in the following case using variables, constants and arithmetic operations.

Sum of numbers a and b subtracted from their product.

Factorize x( x - 2)( x - 4) + 4x - 8

Factorize `2a^2 + 2 sqrt6ab + 3b^2`

Factorize `x^2 - 2sqrt2x - 30`

Factorize the following expressions:

`8x^2y^3 - x^5`

Factorize a^{3} x^{3} - 3a2bx^{2} + 3ab^{2} x - b^{3}

(2x - 3y)^{3} + (4z - 2x)^{3} + (3y - 4z )^{3}

If x + y = 4 and xy = 2, find the value of x^{2} + y^{2}

If 3x + 5y = 11 and xy = 2, find the value of 9x^{2}^{ }+ 25y^{2}

Find the value of the following expression: 16*x*^{2} + 24*x* + 9, when \[x = \frac{7}{4}\]

If x^{2} + y^{2} = 29 and xy = 2, find the value of *x + y.*

If x^{2} + y^{2} = 29 and xy = 2, find the value of *x - y.*

If x^{2} + y^{2} = 29 and xy = 2, find the value of *x*^{4} + *y*^{4 }.

What must be added to the following expression to make it a whole square?

4x^{2} − 12x + 7

27*x*^{3} − *y*^{3} − *z*^{3} − 9*xyz*

If a^{2} + b^{2} + c^{2} = 20 and a + b + c = 0, find ab + bc + ca.

Write the value of 30^{3} + 20^{3} − 50^{3}.

The expression x^{4} + 4 can be factorized as

**Separate the constants and variables from the following :**

`-7,7+"x",7"x"+"yz",sqrt5,sqrt("xy"),(3"yz")/8,4.5"y"-3"x",`

8 −5, 8 − 5x, 8x −5y × p and 3y^{2}z ÷ 4x

Write the number of the term of the following polynomial.

5x^{2} + 3 x ax

Write the number of the term of the following polynomial.

ax ÷ 4 – 7

Write the number of the term of the following polynomial.

ax – by + y x z

Write the number of the term of the following polynomial.

23 + a x b ÷ 2

**Separate monomials, binomials, trinomials and polynomials from the following algebraic expressions :**

8 − 3x, xy^{2}, 3y^{2} − 5y + 8, 9x − 3x^{2} + 15x^{3} − 7,

3x × 5y, 3x ÷ 5y, 2y ÷ 7 + 3x − 7 and 4 − ax^{2} + bx + y

Evaluate: (4m - 2)(m^{2} + 5m - 6)

Evaluate: (4x^{2} - 4x + 1)(2x^{3} - 3x^{2} + 2)

Evaluate: - 4y (15 + 12y - 8z) (x - 2y)

Multiply: (2x + 3y)(2x + 3y)

Divide: 8x + 24 by 4

Divide: n^{2} - 2n + 1 by n - 1

Divide: 4a^{2} + 4a + 1 by 2a + 1

The area of a rectangular field is 25x2 + 20xy + 3y2 square unit. If its length is 5x + 3y unit, find its breadth, Hence find its perimeter.

Divide: 10x^{3}y - 9xy^{2} - 4x^{2}y^{2} by xy

Divide: 3y^{3} - 9ay^{2} - 6ab^{2}y by -3y

Write in the form of an algebraic expression:

Perimeter (P) of a rectangle is two times the sum of its length (l) and its breadth (b).

Write in the form of an algebraic expression:

Perimeter (P) of a square is four times its side.

Write in the form of an algebraic expression:

Area of a square is square of its side.

Express the following as an algebraic expression:

The sum of x and y minus m.

Express the following as an algebraic expression:

The product of x and y divided by m.

Express the following as an algebraic expression:

The subtraction of 5m from 3n and then adding 9p to it.

Express the following as an algebraic expression:

The product of 12, x, y and z minus the product of 5, m and n.

Express the following as an algebraic expression:

Sum of p and 2r – s minus sum of a and 3n + 4x.

**Construct a formula for the following:**

Total wages (₹ W) of a man whose basic wage is (₹ B) for t hours week plus (₹ R) per hour, if he Works a total of T hours.

Find the average (A) of four quantities p, q, r and s. If A = 6, p = 3, q = 5 and r = 7; find the value of s.

**Solve the following equation.**

4(x + 12) = 8

**Solve the following equation.**

3y + 4 = 5y - 6

**Choose the right answer from the option.**

The simplest form of 5 ÷ `(3/2) - 1/3` is _______.

**Choose the right answer from the option.**

The solution of the equation `"3x" - 1/2 = 5/2 + "x"` is _____.

**Choose the right answer from the option.**

Which of the following expressions has the value 37?

Write the coefficient of x^{2} and x in the following polynomials

`4 + 2/5x^2 - 3x`

Write the coefficient of x^{2} and x in the following polynomials

`6 - 2x^2 + 3x^3 - sqrt(7)x`

Write the coefficient of x^{2} and x in the following polynomials

πx^{2} – x + 2

Write the coefficient of x^{2} and x in the following polynomials

`sqrt(3)x^2 + sqrt(2)x + 0.5`

Write the coefficient of x^{2} and x in the following polynomials

`x^2 - 7/2 x + 8`

Complete the table.

× | 2x^{2} |
−2xy | x^{4}y^{3} |
2xyz | (___)xz^{2} |

x^{4} |
|||||

(___) | 4x^{5}y^{4} |
||||

−x^{2}y |
|||||

2y^{2}z |
−10xy^{2}z^{3} |
||||

−3xyz | |||||

(___) | −14xyz^{2} |

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

The variable in the expression 16x – 7 is __________

The constant term of the expression 2y – 6 is _________

When y = –1, the value of the expression 2y – 1 is 3

Write the variables, constant and terms of the following expression

18 + x – y

Write the variables, constant and terms of the following expression

29x + 13y

Write the variables, constant and terms of the following expression

b + 2

If x = 2 and y = 3, then find the value of the following expressions

x + y

If x = 2 and y = 3, then find the value of the following expressions

4y – x

If x = 2 and y = 3, then find the value of the following expressions

x + 1 – y

An algebraic statement which is equivalent to the verbal statement “Three times the sum of ‘x’ and ‘y’ is

The value of 7a – 4b when a = 3, b = 2 is

Give an algebraic equation for the following statement:

“The difference between the area and perimeter of a rectangle is 20”.

3p^{2} – 5pq + 2q^{2} + 6pq – q^{2} + pq is a

Number of terms in the expression a^{2} + bc × d is ______.

An equation is true for all values of its variables.

The figure shows the dimensions of a wall having a window and a door of a room. Write an algebraic expression for the area of the wall to be painted.

The value of 3x^{2} – 5x + 3 when x = 1 is ______.

In the formula, area of circle = πr^{2}, the numerical constant of the expression πr^{2} is ______.

In the expression 2πr, the algebraic variable is ______.

If Rohit has 5xy toffees and Shantanu has 20yx toffees, then Shantanu has ______ more toffees.

Sonu and Raj have to collect different kinds of leaves for science project. They go to a park where Sonu collects 12 leaves and Raj collects x leaves. After some time Sonu loses 3 leaves and Raj collects 2x leaves. Write an algebraic expression to find the total number of leaves collected by both of them.

A school has a rectangular playground with length x and breadth y and a square lawn with side x as shown in the figure given below. What is the total perimeter of both of them combined together?

A student wrote an algebraic expression for “5 less than a number n divided by 3” as `n/3 - 5`. What error did the student make?

Shashi used addition to solve a word problem about the weekly cost of commuting by toll tax for ₹ 15 each day. Ravi solved the same problem by multiplying. They both got the correct answer. How is this possible?

Express the following properties with variables x, y and z.

Commutative property of addition