Question

Factorise 16-a^2-2ab-b^2

Answer 1

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Answer 2

The factorisation of $16-a^2-2ab-b^2=(4+a+b)(4-a-b)$

Step-by-step explanation:

We have,

$16-a^2-2ab-b^2$

To find, the factorisation of $16-a^2-2ab-b^2=?$

∴ $16-a^2-2ab-b^2$

$=4^2-(a^2+2ab+b^2)$

$=4^2-(a+b)^2$

Using algebraic identity,

$(x+y)^2=x^2+2xy+y^2$

$=[4+(a+b)][4-(a+b)]$

Using algebraic identity,

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

$=(4+a+b)(4-a-b)$

Hence, the factorisation of $16-a^2-2ab-b^2=(4+a+b)(4-a-b)$