Question

Find the product of (x+2)(x-2)(x²-4) using suitable identities​

Answer 1

$\huge\frak{\color{red}{Answer:-}}$

${x}^{4} + 16 - 8 {x}^{2}$

$\large\bold\color{tan}{\underbrace{Explanation}:-}$

We can use an identity as:-

$(a + b)(a- b) = {a}^{2} - {b}^{2}$

Here,

$(x + 2)(x - 2)( {x}^{2} - 4)$

$= > ({(x)}^{2} - {(2)}^{2} )( {x}^{2} - 4)$

$= > ( {x}^{2} - 4)( {x }^{2} - 4)$

$= > {( {x}^{2} - 4)}^{2}$

Now, we have to use an identity as :-

${(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab$

Applying all the values :-

${( {x}^{2} - 4)}^{2} = {(( {x}^{2} )}^{2} + {(4)}^{2} - 2( {x}^{2} )(4))$

$= > {x}^{4} + 16 - 8 {x}^{2}$

After all :-

$(x + 2)(x - 2)( {x}^{2} - 4) = {x}^{4} + 16 - 8 {x}^{2}$

or, by rearranging terms:-

$(x + 2)(x - 2)( {x}^{2} - 4) = {x}^{4} - 8 {x}^{2} + 16$