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

The solution to (2a-c)^2-(a+c)^2 is 3a^2-6ac

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

simplify

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

3 a^{2} - 6 a c

Solution steps

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

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

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

Add similar elements:

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

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

Add similar elements:

- 4 a c - 2 a c = - 6 a c

= 3 a^{2} - 6 a c

\frac{3 x ^{4}}{- 9 x ^{5}}

10201

1 - (\frac{1}{2})

\frac{16}{25}

x^{2} + 1 + 2 x