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

The solution to 4x^2+[-(x^2-xy)+(-3y^2+2xy)-(-3x^2+y^2)] is 6x^2+3xy-4y^2

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simplify 4x^2+[-(x^2-xy)+(-3y^2+2xy)-(-3x^2+y^2)]

simplify

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

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

Solution steps

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

Simplify

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

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

- (x^{2} - x y) = - x^{2} + x y

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

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

Group like terms

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

Add similar elements:

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

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

Add similar elements:

x y + 2 x y = 3 x y

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

Add similar elements:

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

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

- 3 - \frac{1}{3}

\frac{x ^{2}}{1}

\frac{x - 3}{4} - \frac{x + 2}{8}

5 x - (2 x - 5)

\frac{3 i ^{30} - i ^{19}}{2 i - 1}

What is 4x^2+[-(x^2-xy)+(-3y^2+2xy)-(-3x^2+y^2)] ?
The solution to 4x^2+[-(x^2-xy)+(-3y^2+2xy)-(-3x^2+y^2)] is 6x^2+3xy-4y^2