Question

expand the following by using suitable formula (3x-y)³​

Answer 1

Answer:

(3x−2y) ³

3 =27x 3 −8y 3 −54x 2y+36xy 2

step-by-step explanation:

Given : Expression (3x-2y)^3(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)(a−b) 3 =a 3 −b3−3ab(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 =(3x)3 −(2y) 3 −3(3x)(2y)(3x−2y)

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

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

3

=27x 3 −8y 3 −54x 2 y+36xy2

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

=27x 3

−8y 3 −54x 2 y+36xy 2