What will be the factors of (a^2+2ab+b^2-c^2)?

Correct answer: (a+b-c)(a+b+c)

The correct answer is A: \((a+b-c)(a+b+c)\). First use the perfect-square identity \(a^2+2ab+b^2=(a+b)^2\). The expression therefore becomes \((a+b)^2-c^2\). Now apply the difference-of-squares identity \(X^2-Y^2=(X-Y)(X+Y)\), taking \(X=a+b\) and \(Y=c\). This gives \((a+b-c)(a+b+c)\). Option A is correct because expanding the conjugate factors returns \((a+b)^2-c^2\), which is the original expression. Option B uses \(a-b\) instead of \(a+b\), so its middle term would be \(-2ab\). Option C is incomplete: it has only one factor and contains \(c\) rather than \(c^2\). Option D is only another unfactorised arrangement; \((a+c)(a-c)=a^2-c^2\), so the full expression is not presented as the required product of factors. Memory cue: complete the perfect square first, then use difference of squares.