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

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

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

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

short formula wrote:What is the formula for short multiplication of the following expression: $$(a + b + c)^2 = ?$$

the formula is $$(a + b + c)^2 = a^2+b^2+c^2+2ab+2ac+2bc$$
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
Guest

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

Hi

You can use $$(a+b+c)^2=(a+b+c)(a+b+c)$$

$$(a+b+c)^2=(a+b+c)(a+b+c)=a(a+b+c)+b(a+b+c)+c(a+b+c)$$

$$=a^2+ab+ac+ab+b^2+bc+ac+bc+c^2$$

$$=a^2+b^2+c^2+2ab+2ac+2bc$$

Faraj Razem

razemsoft21

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

(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
Guest

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

What about $$(a-b+c)^2,(a+b-c)^2,(a-b-c)^2,(b+c-a)^2$$ ?

perfectmath

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

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

leesajohnson

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