Question

Find each of the following products:
(i) $(x+6)(x+6)$
(ii) $(4x+5y)(4x+5y)$
(iii) $(7a+9b)(7a+9b)$
(iv) $(\frac{2}{3}x+\frac{4}{5}y)(\frac{2}{3}x+\frac{4}{5}y)$
(v) $(x^2+7)(x^2+7)$
(vi) $(\frac{5}{6}{a}^2+2)(\frac{5}{6}{a}^2+2)$

Answer 1

Find each of the following products:
(i) $(x+6)(x+6)=(x+6)=(x+6{)}^2=(x{)}^2+2\times x\times 6+(6{)}^2=x^2+12x+36$

(ii) $(4x+5y)(4x+5y)=(4x{)}^2+2\times 4x\times 5y+(5y{)}^2=16x^2+40xy+25y^2$

(iii) $(7a+9b)(7a+9b)=(7a+9b{)}^2(7a{)}^2+2\times 7a\times 9b+(9b{)}^2=49a^2+126ab+81b^2$

(iv) $(\frac{2}{3}x+\frac{4}{5}y)(\frac{2}{3}x+\frac{4}{5}y)={(\frac{2}{3}x+\frac{4}{5}y)}^2={\left(\frac{2}{3}x\right)}^2+2\times \frac{2}{3}x\times \frac{4}{5}y+{\left(\frac{4}{5}\right)}^2=\frac{9}{4}{x}^2+\frac{16}{15}xy+\frac{16}{25}{y}^2$

(v) $(x^2+7)(x^2+7)=(x^2+7{)}^2=(x^2{)}^2+2\times x^2\times 7+(7{)}^2=x^4+14x^2+49$

(vi) $(\frac{5}{6}{a}^2+2)(\frac{5}{6}{a}^2+2)={(\frac{5}{6}{a}^2+2)}^2={\left(\frac{5}{6}{a}^2\right)}^2+2\left(\frac{5}{6}{a}^2\right)\times 2+(2{)}^2=\frac{25}{36}{a}^4+\frac{10}{3}{a}^2+4$