Question

simplify: (2a+3b)³-(2a-3b)³​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

$18b(4a^2 + 3b^2)$

Step-by-step explanation:

Given Expression:

(2a+3b)³-(2a-3b)³​

The expression is in the form $a^3 - b^3$, where

a = (2a + 3b)

b = (2a - 3b)

We know from the various identity formulae that

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

Simplifying the given expression,

(2a+3b)³-(2a-3b)³​

⇒ $[(2a + 3b) - (2a - 3b][(2a + 3b)^2 + (2a + 3b)(2a - 3b) + (2a - 3b)^2]$

⇒ $[2a + 3b - 2a + 3b][(2a + 3b)^2 + (2a + 3b)(2a - 3b) + (2a - 3b)^2]$

From the identity formulae, we also know that

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

We can use these to further simplify the given expression.

We will get

$6b[(2a)^2 + (3b)^2 + 2(2a)(3b) + (2a)^2 - (3b)2^ + (2a)^2 + (3b)^2 - 2(2a)(3b)]$

⇒ $6b[4a^2 + 9b^2 + 12ab + 4a^2 - 9b^2 + 4a^2 + 9b^2 - 12ab]$

⇒ $6b[4a^2 + 4a^2 + 4a^2 + 9b^2]$

⇒ $6b(12a^2 + 9b^2)$

From the expression in the bracket, take 3 common.

We will get

$6b\times3(12a^2 + 9b^2)$

⇒ $18b(4a^2 + 3b^2)$