Question

Solve this:

1. Factorise

(i) (a+b)² +4ab
​(ii) (x²-2xy+y²) -z²
(iii) x⁴-y⁴

Answer 1

$$\begin{gathered} \left(2\right). \\ \left({\mathrm{x}}^2-2\mathrm{xy}+{\mathrm{y}}^2\right)-{\mathrm{z}}^2 \\ ={\left(\mathrm{x}-\mathrm{y}\right)}^2-{\left(\mathrm{z}\right)}^2 \\ =\left(\mathrm{x}-\mathrm{y}+\mathrm{z}\right)\left(\mathrm{x}-\mathrm{y}-\mathrm{z}\right) \\ \left(3\right). \\ {\mathrm{x}}^4-{\mathrm{y}}^4 \\ ={\left({\mathrm{x}}^2\right)}^2-{\left({\mathrm{y}}^2\right)}^2 \\ =\left({\mathrm{x}}^2-{\mathrm{y}}^2\right)\left({\mathrm{x}}^2+{\mathrm{y}}^2\right) \\ =\left(\mathrm{x}+\mathrm{y}\right)\left(\mathrm{x}-\mathrm{y}\right)\left({\mathrm{x}}^2+{\mathrm{y}}^2\right) \end{gathered}$$