What is factor 3(x-y)^2+2y(x-y)-5y^2 ?

The solution to factor 3(x-y)^2+2y(x-y)-5y^2 is -(3x+2y)(-x+2y)

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factor 3(x-y)^2+2y(x-y)-5y^2

factor

3 (x - y)^{2} + 2 y (x - y) - 5 y^{2}

- (3 x + 2 y) (- x + 2 y)

Solution steps

3 (x - y)^{2} + 2 y (x - y) - 5 y^{2}

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

= 3 (x^{2} - 2 x y + y^{2}) + 2 y (x - y) - 5 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 y (x - y) - 5 y^{2}

Expand

2 y (x - y) : 2 x y - 2 y^{2}

= 3 x^{2} - 6 x y + 3 y^{2} + 2 x y - 2 y^{2} - 5 y^{2}

Simplify

3 x^{2} - 6 x y + 3 y^{2} + 2 x y - 2 y^{2} - 5 y^{2} : - 4 y^{2} - 4 x y + 3 x^{2}

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

Factor out common term

- 1

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

Factor

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

= - (3 x + 2 y) (- x + 2 y)

\frac{2}{3} (\frac{x}{8} - \frac{3}{4}) = \frac{x}{2} - \frac{1}{12}

(x - 7) (4 - x) (x + 1) \geq 0

\frac{0.9273}{\frac{π}{45}}

\frac{2 a}{3} - \frac{3 a}{2} = - \frac{5}{2}

x (6 x - 11) > 0

What is factor 3(x-y)^2+2y(x-y)-5y^2 ?
The solution to factor 3(x-y)^2+2y(x-y)-5y^2 is -(3x+2y)(-x+2y)