Question

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

Answer 1

GIVEN :

The expression is $(2a-3b^2)^3$

TO FIND :

The simplified form of the given expression.

SOLUTION :

Given that the expression is $(2a-3b^2)^3$

Now simplify the given expression as below :

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

Expanding the expression by using the formula,

By using the Algebraic identity:

$(a-b)^3=a^3-3a^2b+3ab^2-b^3$

$=(2a)^3-3(2a)^2(3b^2)+3(2a)(3b^2)^2-(3b^2)^3$ here a=2a and $b=3b^2$

$=8a^3-3(4a^2)(3b^2)+3(2a)(9b^4)-(27b^6)$

$=8a^3-36a^2b^2+54ab^4-27b^6$

$=4a^2(2a-9b^2)+27b^4(2a-b^2)$

By taking the common factors we get,

∴  $(2a-3b^2)^3=4a^2(2a-9b^2)+27b^4(2a-b^2)$

∴ the simplified expression to the given expression  $(2a-3b^2)^3$ is  $4a^2(2a-9b^2)+27b^4(2a-b^2)$