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

The solution to 3(x^2-2xy+y^2)-(2xy-x^2+2y^2) is 4x^2-8xy+y^2

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

simplify

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

4 x^{2} - 8 x y + y^{2}

Solution steps

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

Apply the distributive law:

- (a - b) = - a + b

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

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

Expand

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

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

Group like terms

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

Add similar elements:

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

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

Add similar elements:

- 6 x y - 2 x y = - 8 x y

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

Add similar elements:

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

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

(12 m + 3) - (10 m - 6)

(- x^{2} + x) + (4 x^{2} - x - 1)

\frac{1}{s + 4} + 2

(\frac{1}{x}) d x

(5 x^{2} + 4 x + 1) + (- 7 x + 2)

What is 3(x^2-2xy+y^2)-(2xy-x^2+2y^2) ?
The solution to 3(x^2-2xy+y^2)-(2xy-x^2+2y^2) is 4x^2-8xy+y^2