Question

(3x-2y)^3 in expanded form

Answer 1

by using identity (a-b)^3 =(a^3-b^3-3a^2b+ab^2)

( 3 x )^3 -( 2y)^3 -3(3x)^2(2y)+3(3x)(2y)^2

27x^3 -8y^3 -54x^2y + 36xy^2

Answer 2

$(3x-2y)^3=27x^3-8y^3-54x^2y+36xy^2$

Step-by-step explanation:

Given : Expression $(3x-2y)^3$

To find : Write the expression in expanded form ?

Solution :

Using algebraic identity,

$(a-b)^3=a^3-b^3-3ab(a-b)$

Here, a=3x and b=2y

Substitute the values,

$(3x-2y)^3=(3x)^3-(2y)^3-3(3x)(2y)(3x-2y)$

$(3x-2y)^3=27x^3-8y^3-18xy(3x-2y)$

$(3x-2y)^3=27x^3-8y^3-54x^2y+36xy^2$

Therefore, the expanded form is $(3x-2y)^3=27x^3-8y^3-54x^2y+36xy^2$

#Learn more

"Question 6 Write the following cubes in expanded form:

(i) (2x + 1)^3

(ii) (2a - 3b)^3

(iii) [3x/2 + 1]^3

(iv) [x - 2y/3]^3

Class 9 - Math - Polynomials Page 49"

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