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

The solution to (2a+b-c)^2-(a+b)^2 is 3a^2-2bc+2ab-4ac+c^2

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

simplify

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

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

Solution steps

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

Expand

(2 a + b - c)^{2} : 4 a^{2} - 2 b c + 4 ab - 4 a c + b^{2} + c^{2}

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

Expand

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

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

Group like terms

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

Add similar elements:

4 a^{2} - a^{2} = 3 a^{2}

= 3 a^{2} - 2 b c + 4 ab - 2 ab - 4 a c + b^{2} - b^{2} + c^{2}

Add similar elements:

4 ab - 2 ab = 2 ab

= 3 a^{2} - 2 b c + 2 ab - 4 a c + b^{2} - b^{2} + c^{2}

Add similar elements:

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

= 3 a^{2} - 2 b c + 2 ab - 4 a c + c^{2}

(3 x^{4} - 5 x^{3} y)^{3}

\frac{63}{5}

- 6 y + 6 y

\frac{5 p ^{7}}{25 p ^{4}}

\frac{6 ^{17}}{6 ^{24}}

What is (2a+b-c)^2-(a+b)^2 ?
The solution to (2a+b-c)^2-(a+b)^2 is 3a^2-2bc+2ab-4ac+c^2