Question

simplify (a+b+c)^2-(a-b+c)^2

Answer 1

Given to simplify :-

( a + b + c)² - ( a - b + c)²

SOLUTION:-

First we shall expand it

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

( a - b + c )² = a² + b² + c² + 2(a)(-b) + 2(-b)(c) + 2(c)(a)

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

Now Subtracting the (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 + 2ab + 2bc + 2bc

4ab + 4bc

4( ab + bc)

KNOW MORE :-

(a+ b)² = a² + b² + 2ab

( a - b )² = a² + b² - 2ab

( a + b )² + ( a - b)² = 2a² + 2b²

( a + b )² - ( a - b)² = 4ab

a² + b² = ( a + b)² - 2ab

(a + b )³ = a³ + b³ + 3ab ( a + b)

( a - b)³ = a³ - b³ - 3ab ( a - b)

If a + b + c = 0 then a³ + b³ + c³ = 3abc