Question

Question 28
Expand the following
(i) $(4a-b+2c{)}^2$

(ii) $(3a–5b–c{)}^2$

(iii) $(-x+2y-3z{)}^2$

Answer 1

(i)
$(4a-b+2c{)}^2=(4a^2)+(-b{)}^2+(2c{)}^2+2(4a\left)\right(-b)+2(-b\left)\right(2c)+2(2c\left)\right(4a)$
$[Usingtheidentity,(a+b+c{)}^2=a^2+b^2+c^2+2ab+2bc+2ca]$
$=16a^2+b^2+4c^2–8ab–4bc+16ac$

(ii)
$(3a–5b–c{)}^2=(3a{)}^2+(-5b{)}^2+(-c{)}^2+2\left(3a\right)(-5b)+2\left(5b\right)(-c)+2(-c)\left(3a\right)$
$[Usingtheidentity,(a+b+c{)}^2=a^2+b^2+c^2+2ab+2bc+2ca]$
$=9a^2+25b^2+c^2–30ab-10bc–6ac$

(iii)
$(-x+2y-3z{)}^2=(-x{)}^2+(2y{)}^2+(-3z{)}^2+2(-x)\left(2y\right)+2\left(2y\right)(-3z)+2(-3z)(-x)$
$[Usingtheidentity,(a+b+c{)}^2=a^2+b^2+c^2+2ab+2bc+2ca]$
$=x^2+4y^2+9z^2–4xy–12yz+6xz$