Question

[ (2a²+3b²) (a²+b²)] - [ (a²-b²)]² =​

Answer 1

a⁴-2b⁴+7a²b²

this is your answer

Answer 2

Given:

Given expression is $[ (2a^2+3b^2) (a^2+b^2)] - [ (a^2-b^2)]^2$.

To find:

We should find the value of given expression.

Solution:

To find the value of given expression, we need to simplify it.

Consider the given expression,

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

The above expression can be written as,

$\Rightarrow [ (2a^2+3b^2) (a^2+b^2)] - [ (a^2-b^2)]\times [ (a^2-b^2)]$

$\Rightarrow [ (2a^2+3b^2) (a^2+b^2)] - (a^2-b^2)\times (a^2-b^2)$

Multiply the terms,

$\Rightarrow [ 2{a^2}\times a^2+2a^2\times b^2+3b^2\times a^2+3b^2\times b^2] - (a^2-b^2)\times (a^2-b^2)$

Again,

$\Rightarrow [ 2{a^2}\times a^2+2a^2\times b^2+3b^2\times a^2+3b^2\times b^2] - (a^2\times a^2+a^2\times(-b^2)-b^2\times a^2-b^2\times(-b^2))$

Simplifying the terms,

$\Rightarrow [ 2{a^2}\times a^2+2a^2\times b^2+3b^2\times a^2+3b^2\times b^2] - (a^2\times a^2-a^2\times b^2-b^2\times a^2+b^2\times b^2)$

Multiplying the terms,

$\Rightarrow [ 2{a^4}+2a^2 b^2+3b^2a^2+3b^4] - (a^4-a^2 b^2-b^2a^2+b^4)$

$\Rightarrow [ 2{a^4}+2a^2 b^2+3a^2b^2+3b^4] - (a^4-a^2 b^2-a^2b^2+b^4)$

Adding the identical terms,

$\Rightarrow [ 2{a^4}+5a^2 b^2+3b^4] - (a^4-2a^2 b^2+b^4)$

Removing the brackets,

$\Rightarrow 2{a^4}+5a^2 b^2+3b^4 - a^4+2a^2 b^2-b^4$

Rearranging the terms,

$\Rightarrow 2{a^4} - a^4+5a^2 b^2+2a^2 b^2+3b^4-b^4$

Simplifying the above expression,

$\Rightarrow {a^4}+7a^2 b^2+2b^4$

The above expression cannot be simplified further because there are no common terms.

Therefore, the value of given expression is ${a^4}+7a^2 b^2+2b^4$.