1.

Factorise completely x⁴-16​

Answer»

Question :

Factorise \mathtt{x^4-16}

\begin {gathered} \end {gathered}

Answer :

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

\begin {gathered} \end {gathered}

STEP - by - Step EXPLANATION :

We have,

\begin {aligned} (1) \ \bold {x^4 - 16} &\Rightarrow [(x^2)^2 - 4^2]\\\\&[\text{Using <klux>IDENTITY</klux> $a^2 - b^2 = (a + b)(a- b)$}]\\\\&= \bf (x^2 + 4)(x^2 - 4)\end {aligned}

\begin {gathered} \end {gathered}

This can further be Factorised by using the Same Identity GIVEN above . . .

\begin {aligned} (2) \ \bold {(x^2 + 4)(x^2 - 4)} &\Rightarrow \Big [(x^2 + 4)[(x)^2 - 2^2]\Big ]\\\\&= \bf \Big [(x^2 + 4)(x + 2)(x - 2)\Big ] \end {aligned}


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