Question

`a^(2) - b ^(2) + 4b - 4`
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Answer 1

`\left(a+b-2\right)\left(a-b+2\right)`

Explanation:

`a^2-b^2+4b-4`

`a^2-\left(b^2-4b+4\right)`

`a^2-(b^2-2b-2b+4)`

`a^2-\left(b-2\right)\left(b-2\right)`

`a^2-\left(b-2\right)^2`

Apply the difference of two squares formula.

`x^2-y^2=(x+y)(x-y)`

`\left(a+\left(b-2\right)\right)\left(a-\left(b-2\right)\right)`

`\left(a+b-2\right)\left(a+2-b\right)`