What is (a+b+c)^2-(a-b+c)^2 ?

The solution to (a+b+c)^2-(a-b+c)^2 is 4ab+4bc

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

simplify

(a + b + c)^{2} - (a - b + c)^{2}

4 ab + 4 b c

Solution steps

(a + b + c)^{2} - (a - b + c)^{2}

Expand

(a + b + c)^{2} : a^{2} + 2 ab + 2 a c + b^{2} + 2 b c + c^{2}

= a^{2} + 2 ab + 2 a c + b^{2} + 2 b c + c^{2} - (a - b + c)^{2}

Expand

- (a - b + c)^{2} : - a^{2} + 2 ab - 2 a c - b^{2} + 2 b c - c^{2}

= a^{2} + 2 ab + 2 a c + b^{2} + 2 b c + c^{2} - a^{2} + 2 ab - 2 a c - b^{2} + 2 b c - c^{2}

Group like terms

= a^{2} - a^{2} + 2 ab + 2 ab + 2 a c - 2 a c + b^{2} - b^{2} + 2 b c + 2 b c + c^{2} - c^{2}

Add similar elements:

a^{2} - a^{2} = 0

= 2 ab + 2 ab + 2 a c - 2 a c + b^{2} - b^{2} + 2 b c + 2 b c + c^{2} - c^{2}

Add similar elements:

2 ab + 2 ab = 4 ab

= 4 ab + 2 a c - 2 a c + b^{2} - b^{2} + 2 b c + 2 b c + c^{2} - c^{2}

Add similar elements:

2 a c - 2 a c = 0

= 4 ab + b^{2} - b^{2} + 2 b c + 2 b c + c^{2} - c^{2}

Add similar elements:

b^{2} - b^{2} = 0

= 4 ab + 2 b c + 2 b c + c^{2} - c^{2}

Add similar elements:

2 b c + 2 b c = 4 b c

= 4 ab + 4 b c + c^{2} - c^{2}

Add similar elements:

c^{2} - c^{2} = 0

= 4 ab + 4 b c

(10 x - y + 4) - [- (- 7 x - 21 + 3 y) - (- 3 (- 11 y + 9 x - 5))]

\frac{6 x ^{2}}{x - 1} + \frac{- 6 x}{x - 1}

10 x^{3} - 2 sec^{2} (x)

\frac{e ^{4}}{e ^{- 1} + e ^{- 2}}

(448)^{3}