Question

factorise a^2 b^2-a^2-b^2+1

Answer 1

Step-by-step explanation:

Given:-

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

To find:-

factorise a^2 b^2-a^2-b^2+1

Solution:-

Given expression is a^2 b^2-a^2-b^2+1

It can be written as

(a^2b^2-a^2)-(b^2-1)

=>a^2(b^2-1)-(b^2-1)

=>(b^2-1)(a^2-1)

we know that (a+b)(a-b)=a^2-b^2

=>(b+1)(b-1)(a+1)(a-1)

(Therefore, (a+1)(a-1)(b+1)(b-1)

Answer:-

Factorization of a^2 b^2-a^2-b^2+1

is (a+1)(a-1)(b+1)(b-1)

Used formula:-

• (a+b)(a-b)=a^2-b^2