What is factor a^2*b^2-a^2-b^2+1 ?

The solution to factor a^2*b^2-a^2-b^2+1 is (b+1)(b-1)(a+1)(a-1)

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factor a^2*b^2-a^2-b^2+1

factor

a^{2} \cdot b^{2} - a^{2} - b^{2} + 1

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

Solution steps

a^{2} b^{2} - a^{2} - b^{2} + 1

= (a^{2} b^{2} - a^{2}) + (- b^{2} + 1)

Factor out

a^{2}

from

a^{2} b^{2} - a^{2} : a^{2} (b^{2} - 1)

Factor out

- 1

from

- b^{2} + 1 : - (b^{2} - 1)

= a^{2} (b^{2} - 1) - (b^{2} - 1)

Factor out common term

(b^{2} - 1) : (b^{2} - 1) (a^{2} - 1)

= (b^{2} - 1) (a^{2} - 1)

Factor

b^{2} - 1 : (b + 1) (b - 1)

= (b + 1) (b - 1) (a^{2} - 1)

Factor

a^{2} - 1 : (a + 1) (a - 1)

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

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What is factor a^2*b^2-a^2-b^2+1 ?
The solution to factor a^2*b^2-a^2-b^2+1 is (b+1)(b-1)(a+1)(a-1)