Question

how to factorise x^4-16

Answer 1

${\huge {\mathfrak {Answer :-}}}$

✨We have,

${} = x^4 - 16$

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

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

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

Hence, solved.

Answer 2

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

Given : x⁴ - 16

To find : To factorise

Formula : a² – b² = ( a + b ) ( a - b )

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is x⁴ - 16

Step 2 of 2 :

We factorise it as below

$\sf {x}^{4} - 16$

$\sf = {( {x}^{2} )}^{2} - {4}^{2}$

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

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

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

$\sf =(x + 2)(x - 2) ( {x}^{2} + 2)$

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