Factorize the Following Expressions: 32a3 + 108b3 - Mathematics

Advertisements
Advertisements

Factorize the following expressions:

32a3 + 108b3

Advertisements

Solution

32a3 +108b3

= 4(8a3  + 27b3)

= 4((2a)3   + (3b)3)         [Using a3  + b3  = (a + b)(a2  - ab + b2)]

= 4 [(2a + 3b)((2a)2 - 2a x 3b + (3b)2)]

= 4(2a + 3b)(4a2  - 6ab + 9b2)

∴ 32a3   +108b3   = 4(2a + 3b)(4a2 - 6ab + 9b2 )

  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 9 | Page 14

RELATED QUESTIONS

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

Subtraction of z from y


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.

Number 5 added to three times the product of numbers m and n.


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: a2  + b2  + 2 (ab + bc + ca)


Factorize x2 - y2 - 4xz + 4z2


Factorize the following expressions:

y3 +125


Factorize the following expressions:

x4y4 - xy


Factorize 8a3 + 27b3 + 36a2b + 54ab2


Factorize  a3 x3 - 3a2bx2 + 3ab2 x - b3


x3 - 8y3 + 27z3 +18xyz


8x3 -125y3 +180xy + 216


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


If x2 + y2 = 29 and xy = 2, find the value of x4 + y4 .


Multiply: x2 + y2 + z2 − xy + xz + yz by x + y − z


If a2 + b2 + c2 = 250 and ab + bc + ca = 3, find a + b + c.


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: (3x - 1)(4x3 - 2x2 + 6x - 3) 


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


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


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


Divide: 25x2y by - 5y2 


Divide: 4a2 - a by - a 


Divide: x2 + 4xy + 4y2 by x + 2y 


Divide: 15x2 + 31xy + 14y2 by 5x + 7y 


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: x5 - 15x4 - 10x2 by -5x2 


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:

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.


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 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 __________


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


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


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”.


3p2 – 5pq + 2q2 + 6pq – q2 + pq is a


In a polynomial, the exponents of the variables are always ______.


Which of the following is correct?


Number of terms in the expression a2 + 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 3x2 – 5x + 3 when x = 1 is ______.


The total number of planets of Sun can be denoted by the variable n.


A triangle is made up of 2 red sticks and 1 blue sticks . The length of a red stick is given by r and that of a blue stick is given by b. Using this information, write an expression for the total length of sticks in the pattern given below:


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

Commutative property of addition


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

Associative property of addition


Share
Notifications



      Forgot password?
Use app×