What is 3(x+y)^2-4(x-y)^2+3x^2-3y^2 ?

The solution to 3(x+y)^2-4(x-y)^2+3x^2-3y^2 is 2x^2+14xy-4y^2

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simplify 3(x+y)^2-4(x-y)^2+3x^2-3y^2

simplify

3 (x + y)^{2} - 4 (x - y)^{2} + 3 x^{2} - 3 y^{2}

2 x^{2} + 14 x y - 4 y^{2}

Solution steps

3 (x + y)^{2} - 4 (x - y)^{2} + 3 x^{2} - 3 y^{2}

Expand

3 (x + y)^{2} : 3 x^{2} + 6 x y + 3 y^{2}

= 3 x^{2} + 6 x y + 3 y^{2} - 4 (x - y)^{2} + 3 x^{2} - 3 y^{2}

Expand

- 4 (x - y)^{2} : - 4 x^{2} + 8 x y - 4 y^{2}

= 3 x^{2} + 6 x y + 3 y^{2} - 4 x^{2} + 8 x y - 4 y^{2} + 3 x^{2} - 3 y^{2}

Group like terms

= 3 x^{2} - 4 x^{2} + 3 x^{2} + 6 x y + 8 x y + 3 y^{2} - 4 y^{2} - 3 y^{2}

Add similar elements:

3 x^{2} - 4 x^{2} + 3 x^{2} = 2 x^{2}

= 2 x^{2} + 6 x y + 8 x y + 3 y^{2} - 4 y^{2} - 3 y^{2}

Add similar elements:

6 x y + 8 x y = 14 x y

= 2 x^{2} + 14 x y + 3 y^{2} - 4 y^{2} - 3 y^{2}

Add similar elements:

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

= 2 x^{2} + 14 x y - 4 y^{2}

\frac{6}{10} + \frac{3}{7} + \frac{1}{2}

\frac{9 - x ^{2}}{9 x + 27}

(x + i)^{2}

- \frac{59}{10} - (- 6)

\frac{40}{360}

What is 3(x+y)^2-4(x-y)^2+3x^2-3y^2 ?
The solution to 3(x+y)^2-4(x-y)^2+3x^2-3y^2 is 2x^2+14xy-4y^2