Factorise b2+c2+2bc−a2
(b+c+a)(b+c−a)
(b2+c)(c2−a)
(b−c+a)(b+c−a)
(bc+a)(bc−a)
Given: b2+c2+2bc−a2
⇒(b+c)2−a2 (using (a+b)2)
⇒(b+c+a)(b+c−a) (using difference of squares)
If a + b + c = 0, then prove the following
(a) (b + c) (b − c) + a(a + 2b) = 0
(b) a(a2 − bc) + b(b2 − ca) + c(c2 − ab) = 0
(c) a(b2 + c2) + b(c2 + a2) + c(a2 + b2) = −3abc
(d)