Solve [(5x^{2}y)(4/5x^{4}y^{5}-1/2x^{4}y^{5}):(-1/2xy)^3+2x^3y^3]:(-5xy)^2-3/5xy+xy

$$[ ( 5 x ^ { 2 } y ) ( \frac { 4 } { 5 } x ^ { 4 } y ^ { 5 } - \frac { 1 } { 2 } x ^ { 4 } y ^ { 5 } ) : ( - \frac { 1 } { 2 } x y ) ^ { 3 } + 2 x ^ { 3 } y ^ { 3 } ] : ( - 5 x y ) ^ { 2 } - \frac { 3 } { 5 } x y + x y$$

Factor

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Solution Steps

Combine \frac{4}{5}x^{4}y^{5} and -\frac{1}{2}x^{4}y^{5} to get \frac{3}{10}x^{4}y^{5}.

$$factor(\frac{\frac{5x^{2}y\times \frac{3}{10}x^{4}y^{5}}{\left(-\frac{1}{2}xy\right)^{3}}+2x^{3}y^{3}}{\left(-5xy\right)^{2}}-\frac{3}{5}xy+xy)$$

Multiply 5 and \frac{3}{10} to get \frac{3}{2}.

$$factor(\frac{\frac{\frac{3}{2}x^{2}yx^{4}y^{5}}{\left(-\frac{1}{2}xy\right)^{3}}+2x^{3}y^{3}}{\left(-5xy\right)^{2}}-\frac{3}{5}xy+xy)$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$factor(\frac{\frac{\frac{3}{2}x^{6}yy^{5}}{\left(-\frac{1}{2}xy\right)^{3}}+2x^{3}y^{3}}{\left(-5xy\right)^{2}}-\frac{3}{5}xy+xy)$$

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$factor(\frac{\frac{\frac{3}{2}x^{6}y^{6}}{\left(-\frac{1}{2}xy\right)^{3}}+2x^{3}y^{3}}{\left(-5xy\right)^{2}}-\frac{3}{5}xy+xy)$$

Expand \left(-\frac{1}{2}xy\right)^{3}.

$$factor(\frac{\frac{\frac{3}{2}x^{6}y^{6}}{\left(-\frac{1}{2}\right)^{3}x^{3}y^{3}}+2x^{3}y^{3}}{\left(-5xy\right)^{2}}-\frac{3}{5}xy+xy)$$

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$factor(\frac{\frac{\frac{3}{2}x^{6}y^{6}}{-\frac{1}{8}x^{3}y^{3}}+2x^{3}y^{3}}{\left(-5xy\right)^{2}}-\frac{3}{5}xy+xy)$$

Cancel out x^{3}y^{3} in both numerator and denominator.

$$factor(\frac{\frac{\frac{3}{2}x^{3}y^{3}}{-\frac{1}{8}}+2x^{3}y^{3}}{\left(-5xy\right)^{2}}-\frac{3}{5}xy+xy)$$

Divide \frac{3}{2}x^{3}y^{3} by -\frac{1}{8} by multiplying \frac{3}{2}x^{3}y^{3} by the reciprocal of -\frac{1}{8}.

$$factor(\frac{\frac{\frac{3}{2}x^{3}y^{3}\times 8}{-1}+2x^{3}y^{3}}{\left(-5xy\right)^{2}}-\frac{3}{5}xy+xy)$$

Multiply \frac{3}{2} and 8 to get 12.

$$factor(\frac{\frac{12x^{3}y^{3}}{-1}+2x^{3}y^{3}}{\left(-5xy\right)^{2}}-\frac{3}{5}xy+xy)$$

Anything divided by -1 gives its opposite.

$$factor(\frac{-12x^{3}y^{3}+2x^{3}y^{3}}{\left(-5xy\right)^{2}}-\frac{3}{5}xy+xy)$$

Combine -12x^{3}y^{3} and 2x^{3}y^{3} to get -10x^{3}y^{3}.

$$factor(\frac{-10x^{3}y^{3}}{\left(-5xy\right)^{2}}-\frac{3}{5}xy+xy)$$

Expand \left(-5xy\right)^{2}.

$$factor(\frac{-10x^{3}y^{3}}{\left(-5\right)^{2}x^{2}y^{2}}-\frac{3}{5}xy+xy)$$

Calculate -5 to the power of 2 and get 25.

$$factor(\frac{-10x^{3}y^{3}}{25x^{2}y^{2}}-\frac{3}{5}xy+xy)$$

Cancel out 5x^{2}y^{2} in both numerator and denominator.

$$factor(\frac{-2xy}{5}-\frac{3}{5}xy+xy)$$

Combine -\frac{3}{5}xy and xy to get \frac{2}{5}xy.

$$factor(\frac{-2xy}{5}+\frac{2}{5}xy)$$

Factor out \frac{2}{5}.

$$\frac{2\left(-xy+xy\right)}{5}$$

Consider -xy+xy. Factor out xy.

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Evaluate

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