Question

factorise a2(b+c) +b2 (c+a) + c2 (a+b) +2abc
$a {}^{2} (b + c) + b {}^{2} (c + a) + c { }^{2} (a + b) + 2abc$
​

Answer 1

Step-by-step explanation:

a(b

2

+c

2

)+b(c

2

+a

2

)+c(a

2

+b

2

)+2abc

=ab

2

+ac

2

+bc

2

+ba

2

+ca

2

+cb

2

+2abc

=ba

2

+ca

2

+ab

2

+ac

2

+2abc+bc

2

+cb

2

=a

2

(b+c)+a(b

2

+c

2

+2bc)+bc(c+b)

=a

2

(b+c)+(b+c)

2

+bc(b+c)

=(b+c)[(a

2

+a(b+c)+bc]

=(b+c)[a

2

+ab+ac+bc]

=(b+c)[a(a+b)+c(a+b)]

=(b+c)(a+b)(a+c)

=(a+b)(b+c)(c+a)