Question

State True or False.

$\sum a(b^2-c^2)$$=(a-b)(b-c)(c-a)$

• A. True
• B. False

Answer 1

The correct option is A True

Consider, L.H.S. $=\Sigma a(b^2-c^2)$

$=a{b}^2-a{c}^2+b{c}^2-b{a}^2+c{a}^2-c{b}^2$

adding and subracting abc,

$\Rightarrow abc+a{b}^2-a{c}^2+b{c}^2-b{a}^2+c{a}^2-c{b}^2-abc$

$=a(bc-ab-c^2+ac)-b(bc-ab-c^2+ac)$

$=(a-b)(bc-ab-c^2+ac)=(a-b)(b-c)(c-a)$