What is the short multiplication formula for (a + b + c)

[short formula]

What is the formula for short multiplication of the following expression: [tex](a + b + c)^2 = ?[/tex]

[Guest]

What is the formula for short multiplication of the following expression: [tex](a + b + c)^2 = ?[/tex]

the formula is [tex](a + b + c)^2 = a^2+b^2+c^2+2ab+2ac+2bc[/tex]
if you want to know how you can get that conclusion yourself assume that p=a+b and than just use the regular formula (p+c)^2=p^2+c^2+2pc now just replace p with a+b and you will get the formula above

[razemsoft21]

Hi

You can use [tex](a+b+c)^2=(a+b+c)(a+b+c)[/tex]

[tex](a+b+c)^2=(a+b+c)(a+b+c)=a(a+b+c)+b(a+b+c)+c(a+b+c)[/tex]

[tex]=a^2+ab+ac+ab+b^2+bc+ac+bc+c^2[/tex]

[tex]=a^2+b^2+c^2+2ab+2ac+2bc[/tex]

Faraj Razem

[Guest]

(a+b+c)^2
Here is a solution for equation :

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

Now we are multiplying each letter of both multiplier :

a(a+b+c) + b(a+b+c) + c(a+b+c)
=> a^2 + ab + ac + ba + b^2 + bc + ca + cb + c^2
=> a^2 + b^2 + c^2 + 2ab + 2bc + 2ca

[perfectmath]

What about [tex](a-b+c)^2,(a+b-c)^2,(a-b-c)^2,(b+c-a)^2[/tex] ?

[leesajohnson]

Formula for (a+b+c)²
(a+b+c)² = a²+b²+c²+2ab+2bc+2ca

[Guest]

Formula for (a+b+c)²
(a+b+c)² = a²+b²+c²+2ab+2bc+2ca

And for [tex](a+ b- c)^2[/tex] just change the sign on each c: [tex](a+ b- c)^2= a^2+ b^2+ (-c)^2+ 2ab+ 2b(-c)+ 2(-c)a= a^2+ b^2+ c^2+ 2ab- 2bc- 2ca[/tex]

Similarly, [tex](a- b+ c)^2= a^2+ b^2+ c^2- 2ab- 2bc+ 2ca[/tex] and [tex](-a+ b+ c)^2= a^2+ b^2+ c^2- 2ab+ 2bc- 2ca[/tex].

[tex](a- b- c)^2= a^2+ (-b)^2+ (-c)^2+ 2a(-b)+ 2(-b)(-c)+ 2(c)a= a^2+ b^2+ c^2- 2ab+ 2bc- 2ca[/tex]

[GeradHum]

The short multiplication formula is:
(a+b+c)2=a2+b2+c2+2ab+2ac+2bc(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc(a+b+c)2=a2+b2+c2+2ab+2ac+2bc
It's just like squaring a binomial, but with three terms — don't forget the cross terms!