Question

Find
(i) $(x+6)(x+6)$
(ii) $(\frac{2}{3}x+\frac{4}{5}y)(\frac{2}{3}x+\frac{4}{5}y)$

Answer 1

1. $(x+6)(x+6)=x\cdot x+6x+6x+6\cdot 6=x^2+12x+36$
2. $(\frac{2}{3}x+\frac{4}{5}y)(\frac{2}{3}x+\frac{4}{5}y)=\left(\frac{2}{3}x\right)\cdot \left(\frac{2}{3}x\right)+\left(\frac{2}{3}x\right)\left(\frac{4}{5}y\right)+\left(\frac{4}{5}y\right)\left(\frac{2}{3}x\right)+\left(\frac{4}{5}y\right)\cdot \left(\frac{4}{5}y\right)=\frac{4}{9}{x}^2+\frac{8}{15}xy+\frac{8}{15}xy+\frac{!6}{25}{y}^2=\frac{4}{9}{x}^2+\frac{16}{15}xy+\frac{16}{25}{y}^2$