Question

Write the following in the expanded form:

(vii) $(ab+bc+ca{)}^2$

Answer 1

Given,$(ab+bc+ca{)}^2$
Using Identity,
$(a+b+c{)}^2=a^2+b^2+c^2+2ab+2bc+2ca$
$\therefore (ab+bc+ca{)}^2$
$=(ab{)}^2+(bc{)}^2+(ca{)}^2+2\times ab\times bc+2\times bc\times ca+2\times ca\times ab$
$=a^2{b}^2+b^2{c}^2+c^2{a}^2+2a{b}^{2}c+2b{c}^{2}a+2c{a}^{2}b$

Hence, $(ab+bc+ca{)}^2=a^2{b}^2+b^2{c}^2+c^2{a}^2+2a{b}^{2}c+2b{c}^{2}a+2c{a}^{2}b.$