Factorize the Following Expressions: 54x6y + 2x3y4 - Mathematics

Advertisements
Advertisements

Factorize the following expressions:

54x6y + 2x3y4

Advertisements

Solution

54x6 y + 2x3 y4

= 2x3 y (27x3  + y3)

= 2x3 y ((3x)3 + y3)

= 2x3 y (3x + y)((3x)2  - 3 x xy + y2)     [ ∵ a3 + b3  = (a + b)(a2 - ab + b2)]

= 2x3 y (3x + y)(9x2  - 3xy + y2)

∴ 54x6 y + 2x3 y4  = 2x3 y (3x + y )(9x2  - 3xy + y2)

  Is there an error in this question or solution?
Chapter 5: Factorisation of Algebraic Expressions - Exercise 5.2 [Page 14]

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.2 | Q 8 | Page 14

RELATED QUESTIONS

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

The number z multiplied by itself.


Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

One-fourth of the product of numbers p and q.


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 (a - b + c)2 + (b - c + a)2 + 2(a - b + c) (b - c + a)


Factorize `x^2 - 2sqrt2x - 30`


Factorize `x^2 + 2sqrt3x - 24`


Factorize the following expressions:

32a3 + 108b3


Factorize the following expressions:

(a - 2b)3 - 512b3


Factorize 64a3 +125b3 + 240a2b + 300ab2


Factorize 8x3 + 27 y3 + 36x2 y + 54xy2


`2sqrt2a^3 + 3sqrt3b^3 + c^3 - 3 sqrt6abc`


If \[x^2 + \frac{1}{x^2} = 18,\]  find the values of \[x + \frac{1}{x} \text { and } x - \frac{1}{x} .\]


If x + y = 4 and xy = 2, find the value of x2 + y2


If x − y = 7 and xy = 9, find the value of x2 + y2


If 3x + 5y = 11 and xy = 2, find the value of 9x2 + 25y2


Find the value of the following expression:  64x2 + 81y2 + 144xy, when x = 11 and \[y = \frac{4}{3}\]


Find the value of the following expression:  81x2 + 16y2 − 72xy, when \[x = \frac{2}{3}\] and  \[y = \frac{3}{4}\]


If x2 + y2 = 29 and xy = 2, find the value of x + y.


If x2 + y2 = 29 and xy = 2, find the value of x - y.


Write the value of \[\left( \frac{1}{2} \right)^3 + \left( \frac{1}{3} \right)^3 - \left( \frac{5}{6} \right)^3 .\]


Factorize: x4 + x2 + 25.


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 3y2z ÷ 4x


Write the number of the term of the following polynomial.

5x2 + 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, xy2, 3y2 − 5y + 8, 9x − 3x2 + 15x3 − 7,
3x × 5y, 3x ÷ 5y, 2y ÷ 7 + 3x − 7 and 4 − ax2 + bx + y


Evaluate: `(1/2 "a" + 1/2 "b") (1/2 "a" - 1/2 "b")`


Evaluate: (a2 + b2 + c2 - ab - bc - ca)(a + b + c) 


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


Multiply: (2x + 5y + 6)(3x + y - 8)


Divide: 4a2 - a by - a 


Divide: m2 - 2mn + n2 by m - n 


Divide: x2 + 4xy + 4y2 by x + 2y 


The area of a rectangle is 6x2 – 4xy – 10y2 square unit and its length is 2x + 2y unit. Find its breadth.


Divide: x3 - 6x2 + 11x - 6 by x2 - 4x + 3 


Divide: m3 - 4m2 + m + 6 by m2 - m - 2 


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.


Write in the form of an algebraic expression:

Surface area of a cube is six times the square of its edge.


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.


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 x2 and x in the following polynomials

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


Write the coefficient of x2 and x in the following polynomials

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


Write the coefficient of x2 and x in the following polynomials

πx2 – x + 2


Write the coefficient of x2 and x in the following polynomials

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


Write the coefficient of x2 and x in the following polynomials

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


Complete the table.

× 2x2 −2xy x4y3 2xyz (___)xz2
x4          
(___)     4x5y4    
−x2y          
2y2z         −10xy2z3
−3xyz          
(___)       −14xyz2  

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

7p – 4q + 5


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

2x – 3y


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


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”.


3p2 – 5pq + 2q2 + 6pq – q2 + pq is a


Which of the following is correct?


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.


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


Shiv works in a mall and gets paid ₹ 50 per hour. Last week he worked for 7 hours and this week he will work for x hours. Write an algebraic expression for the money paid to him for both the weeks.


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?


In the given figure, the length of a green side is given by g and that of the red side is given by p.


Write an expression for the following pattern. Also write an expression if 100 such shapes are joined 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?


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

Commutative property of addition


Share
Notifications



      Forgot password?
Use app×