What is (6x^2-2y^2-xy)/(y+2x) ?

The solution to (6x^2-2y^2-xy)/(y+2x) is 3x-2y

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simplify (6x^2-2y^2-xy)/(y+2x)

simplify

\frac{6 x ^{2} - 2 y ^{2} - x y}{y + 2 x}

3 x - 2 y

Solution steps

\frac{6 x ^{2} - 2 y ^{2} - x y}{y + 2 x}

Factor

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

= \frac{( 2 x + y ) ( 3 x - 2 y )}{y + 2 x}

Apply the commutative law:

y + 2 x = 2 x + y

= \frac{( 2 x + y ) ( 3 x - 2 y )}{2 x + y}

Cancel the common factor:

2 x + y

= 3 x - 2 y

1 - k^{3}

(1 - cos (x)) (1 - cos (x))

(4 x^{3} y^{2} - 5 x^{2} y^{3} + 6 x^{4} y - 8 x y^{4}) - (12 x^{2} y^{3} - 3 x y^{4} + 4 x^{3} y^{2} - 9 x^{4} y)

\frac{1 - - 1}{1 + - 1}

\frac{5 x}{2 x}