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

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

Postby short formula » Wed Apr 27, 2011 4:35 pm

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

Postby Guest » Thu May 05, 2011 12:41 pm

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

Postby razemsoft21 » Sun May 13, 2012 7:11 am

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 :D

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

Postby Guest » Fri Jun 01, 2012 7:15 am

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

Postby perfectmath » Sat Jun 30, 2012 3:29 am

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

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

Postby leesajohnson » Mon Jan 18, 2016 6:21 am

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