Question

Factorise : $a–b–a^2+b^2$

• A. $(a-b)\left[1-(a+b)\right]$
• B. $(a+b)\left[1-(a-b)\right]$
• C. $(a-b)\left[1-(a-b)\right]$
• D. none of these

Answer 1

The correct option is A

$(a-b)\left[1-(a+b)\right]$

Explanation for correct option:

Factorise the polynomial

$$\begin{gathered} a–b–a^2+b^2 \\ =a-b-1(a^2-b^2) \end{gathered}$$

using the identity $x^2-y^2=(x+y)(x-y)$

$$\begin{gathered} =a-b-(a-b)(a+b) \\ =(a-b)\left[1-(a+b)\right] \end{gathered}$$

Hence, the factors of $a–b–a^2+b^2$ are $(a-b)$ and $(1-(a+b))$.

Therefore, Option A is correct.