Question

Find the product of the following:
(i) $(\frac{4}{3}{x}^2+3)(\frac{4}{3}{x}^2+3)$
(ii) $(\frac{2}{3}{x}^2+5y^2)(\frac{4}{3}{x}^2+5y^2)$

Answer 1

(i) We have, $(\frac{4}{3}{x}^2+3)(\frac{4}{3}{x}^2+3)$
${(\frac{4}{3}{x}^2+3)}^2$ $[a.a=a^2]$
${\left(\frac{4}{3}{x}^2\right)}^2+2\times \frac{4}{3}{x}^2\times 3+(3{)}^2$ [Using: $(a+b{)}^2=a^2+2ab+b^2$]
$=\frac{16}{9}{x}^4+8x^2+9$
(ii) We have,
$(\frac{2}{3}{x}^2+5y^2)(\frac{2}{3}{x}^2+5y^2)$
$={(\frac{2}{3}{x}^2+5y^2)}^2={\left(\frac{2}{3}{x}^2\right)}^2+2\times \frac{2}{3}{x}^2\times 5y^2+(5y^2{)}^2$ [Using: $(a+b{)}^2=a^2+2ab+b^2$]
$=\frac{4}{9}{x}^4+\frac{20}{3}{x}^2{y}^2+25y^4$