Factorize 8a3 + 27b3 + 36a2b + 54ab2 - Mathematics

Advertisements
Advertisements
Answer in Brief

Factorize 8a3 + 27b3 + 36a2b + 54ab2

Advertisements

Solution

The given expression to be factorized is  `8a^3 + 27b^3  + 36a^2 b+ 54ab^2`

This can be written in the form

 `8a^3 + 27b^3 + 36a^2b + 54ab^2 = (2a)^3 + (3b)^3 + 36a^2b + 54ab^2`

Take common 18ab from the last two terms,. Then we get 

`8a^3 + 27b^3 + 36a^2 b+ 54ab^2 = (2a)^3 +(3b)^3+ 18ab(2a + 3b)`

This can be written in the following form

`8a^3 + 27b^3 + 36a^2 b+ 54ab^2 = (2a)^3 +(3b)^3+ 3.2a.3b(2a + 3b)`

Recall the formula for the cube of the sum of two numbers `(a+b)^3 = a^3 + b^3 + 3ab(a+b)`

Using the above formula, we have  `8a^3 + 27b^3 + 36a^2b+ 54ab^2 = (2a +3b)^3`

We cannot further factorize the expression. 

So, the required factorization is of `8a^3 + 27b^3 + 36a^2b+ 54ab^2 " is "(2a +3b)^3` .

  Is there an error in this question or solution?
Chapter 5: Factorisation of Algebraic Expressions - Exercise 5.3 [Page 17]

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.3 | Q 8 | Page 17

RELATED QUESTIONS

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

Subtraction of z from y


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.

Numbers x and y both squared and added.


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.

Product of numbers y and z subtracted from 10.


Factorize (x + 2)(x2 + 25) -10x2 - 20x


Factorize `2x^2 + 3sqrt5x + 5`


Factorize 2( x + y)2 - 9( x + y) - 5


Factorize the following expressions

64a3 – b3


Factorize the following expressions:

x6 + y6


Factorize the following expressions:

a3 + b3 + a + b


Factorize the following expressions:

`a^3 - 1/a^3 - 2a + 2/a`


Factorize the following expressions:

8a3 - b3 - 4ax + 2bx


`1/27 x^3 - y^3 + 125z^3 + 5xyz`


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


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.


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

4x2 − 20x + 20


Write the value of 483 − 303 − 183.


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


Evaluate:

(i) (a + b)(a - b)

(ii) (a2 + b2)(a + b)(a - b); using the result of (i).

(iii) (a4 + b4)(a2 + b2)(a + b)(a - b); using the result of (ii).


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


Multiply: (6x - 2y)(3x - y)


Divide: 8x + 24 by 4


Divide: 9a4b - 15a3b2 + 12a2b3 by - 3a2


Divide: n2 - 2n + 1 by n - 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: 2m3n5 by - mn 


Divide: 12a2 + ax - 6x2 by 3a - 2x 


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:

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 __________


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

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


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.


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


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.


The rate of planting the grass is ₹ x per square metre. Find the cost of planting the grass on a triangular lawn whose base is y metres and height is z metres.


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.

Distributive property of multiplication over addition


Share
Notifications



      Forgot password?
Use app×