Question

Solve the following quadratic equations by factorization:

$2x^2+ax-a^2=0$

Answer 1

$$\begin{gathered} 2x^2+ax-a^2=0 \\ \Rightarrow 2x^2+2ax-ax-a^2=0 \\ \Rightarrow 2x\left(x+a\right)-a\left(x+a\right)=0 \\ \Rightarrow \left(2x-a\right)\left(x+a\right)=0 \\ \Rightarrow 2x-a=0\mathrm{or}x+a=0 \\ \Rightarrow x=\frac{a}{2}\mathrm{or}x=-a \end{gathered}$$

Hence, the factors are $\frac{a}{2}$ and $-a$.