Question

a2b2 - a2 - b2 + 1
Factorise it

Answer 1

a2b2-a2-b2+1=a2(b2-1)-1(b2-1)=(b2-1)(a2-1)

Answer 2

$a^2b^2-a^2-b^2+1 = \left(b+1\right)\left(b-1\right)\left(a+1\right)\left(a-1\right)$

Solution:

Given that,

We have to factorize the following:

$a^2b^2 - a^2 - b^2 + 1$

We have to write as a product of factors

From given,

$a^2b^2 - a^2 - b^2 + 1 \\\\Break\ the\ expression\ into\ groups \\\\\left(a^2b^2-a^2\right)-\left(b^2-1\right) \\\\\mathrm{Factor\:out\:}a^2\mathrm{\:from\:}a^2b^2-a^2\\\\a^2(b^2 - 1) - (b^2 - 1)\\\\\mathrm{Factor\:out\:common\:term\:}b^2-1\\\\\left(b^2-1\right)\left(a^2-1\right) \\\\\mathrm{Factor}\:b^2-1:\quad \left(b+1\right)\left(b-1\right)$

$\left(b+1\right)\left(b-1\right)\left(a^2-1\right)\\\\\mathrm{Factor}\:a^2-1:\quad \left(a+1\right)\left(a-1\right)\\\\\left(b+1\right)\left(b-1\right)\left(a+1\right)\lef$

Thus we have got:

$a^2b^2-a^2-b^2+1 = \left(b+1\right)\left(b-1\right)\left(a+1\right)\left(a-1\right)$

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