Question

simplify (a+b+c)^2 - (a-b+c)^2
With full explanation please​

Answer 1

Answer:

(a+b+c)^2 – (a-b-c)^2

This equation is of the form

x^2 – y^2= (x+y)(x-y)

If we apply this formula for the equation we get

(a+b+c)^2 – (a-b-c)^2

=(a+b+c+a-b-c){a+b+c-(a-b-c)}

=(2a)(a+b+c-a+b+c)

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

=4ab + 4ac

Answer 2

(a + b + c)² - (a - b + c)²

__________ [ GIVEN ]

• We have to simply it.

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We know that

• (a + b)² = a² + b² + 2ab

Now

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

And

=> (a - b + c)² = a² + b² + c² - 2ab + 2bc - 2ca

So ..

→ (a + b + c)² - (a - b + c)² = a² + b² + c² + 2ab + 2bc + 2ca - (a² + b² + c² - 2ab + 2bc - 2ca)

→ a² + b² + c² + 2ab + 2bc + 2ca - a² - b² - c² + 2ab - 2bc + 2ca

→ 2ab + 2ca + 2ab + 2ca

→ 4ab + 4ca

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