factorize: a2+b2-2(ab-ac+bc)

Question

mathslover · Answer

check it again @basith is it : 

$$\large{a^2+b^2+c^2-2(ab-ac+bc)}$$
$$\large{a^2+b^2-c^2-2(ab-ac+bc)}$$

mathslover · Answer

which one?

mathslover · Answer

$${\large(a+b+c)^2 = a^2+b^2+c^2+2(ab+bc+ca)}$$

anonymous · Answer

$$a ^{2}+b ^{2}-2(ab-ac+bc)$$

mathslover · Answer

ok .. : 
$${a^2+b^2-2(ab-ac+bc)=a^2+b^2-2ab+2ac-2bc}$$
$$\large{=a^2-2ab+b^2-2bc+2ac}$$

mathslover · Answer

$$\large{a(a-2b)+b(b-2c)+2ac}$$

neo92 · Answer

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

neo92 · Answer

got it??

mathslover · Answer

$$\large{a^2-2ab+b^2-2bc+2ac}$$
$$\large{(a-b)^2+2c(a-b)}$$
$$\large{(a-b)(a-b+2c)}$$ 

good work @Neo92

mathslover · Answer

@basith got it?

neo92 · Answer

@ mathsolver 
thnx.. i missed da 2 there..

mathslover · Answer

no problem ..

anonymous · Answer

i have a doubt @mathslover

mathslover · Answer

ask @basith

anonymous · Answer

how did u get.....
$$(a-b)(a-b+2c)$$

mathslover · Answer

i took (a-b) common

mathslover · Answer

i was having: 
$$\large{(a-b)^2+2c(a-b)}$$ 
$$\large{(a-b)(a-b)+2c(a-b)}$$
$$\large{(a-b)(a-b+2c)}$$

anonymous · Answer