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

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

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

factor

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

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

Solution steps

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

Factor

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

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

Apply Difference of Two Squares Formula:

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

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

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

Apply rule:

(a) = a

(a + 1) = a + 1

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

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