Question

(a + b) ^ 2 – 2ab = ___________ + ____________.

Answer 1

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$(a + b) {}^{2} - 2ab$

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${(a + b)}^{2} - 2ab \\ = {a}^{2} + {b}^{2} + 2ab - 2ab \\ = {a}^{2} + {b}^{2}$

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Answer 2

Given equation is a

2

−2ab−c

2

+b

2

We can write the given equation as,

⇒ a

2

−2ab+b

2

−c

2

⇒ (a−b)

2

−c

2

....Since (a

2

−2ab+b

2

=(a−b)

2

)

Also we know,

m

2

−n

2

=(m+n)(m−n)

Here, m=(a−b) and n=c

Thus a

2

−2ab−c

2

+b

2

=(a−b+c)(a−b−c)

Factors are (a−b+c) and (a−b−c).

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