Solve [(3y-5y)^{2}(2x^2y^3)]:(-1/2xy^2)^2-[20y-(-8y)]

$$[ ( 3 y - 5 y ) ^ { 2 } ( 2 x ^ { 2 } y ^ { 3 } ) ] : ( - \frac { 1 } { 2 } x y ^ { 2 } ) ^ { 2 } - [ 20 y - ( - 8 y ) ]$$

Evaluate

$$4y$$

Solution Steps

Combine 3y and -5y to get -2y.

$$\frac{\left(-2y\right)^{2}\times 2x^{2}y^{3}}{\left(-\frac{1}{2}xy^{2}\right)^{2}}-\left(20y-\left(-8y\right)\right)$$

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

$$\frac{\left(-2\right)^{2}y^{2}\times 2x^{2}y^{3}}{\left(-\frac{1}{2}xy^{2}\right)^{2}}-\left(20y-\left(-8y\right)\right)$$

Calculate -2 to the power of 2 and get 4.

$$\frac{4y^{2}\times 2x^{2}y^{3}}{\left(-\frac{1}{2}xy^{2}\right)^{2}}-\left(20y-\left(-8y\right)\right)$$

Multiply 4 and 2 to get 8.

$$\frac{8y^{2}x^{2}y^{3}}{\left(-\frac{1}{2}xy^{2}\right)^{2}}-\left(20y-\left(-8y\right)\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{8y^{5}x^{2}}{\left(-\frac{1}{2}xy^{2}\right)^{2}}-\left(20y-\left(-8y\right)\right)$$

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

$$\frac{8y^{5}x^{2}}{\left(-\frac{1}{2}\right)^{2}x^{2}\left(y^{2}\right)^{2}}-\left(20y-\left(-8y\right)\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{8y^{5}x^{2}}{\left(-\frac{1}{2}\right)^{2}x^{2}y^{4}}-\left(20y-\left(-8y\right)\right)$$

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{8y^{5}x^{2}}{\frac{1}{4}x^{2}y^{4}}-\left(20y-\left(-8y\right)\right)$$

Cancel out x^{2}y^{4} in both numerator and denominator.

$$\frac{8y}{\frac{1}{4}}-\left(20y-\left(-8y\right)\right)$$

Divide 8y by \frac{1}{4} by multiplying 8y by the reciprocal of \frac{1}{4}.

$$8y\times 4-\left(20y-\left(-8y\right)\right)$$

The opposite of -8y is 8y.

$$8y\times 4-\left(20y+8y\right)$$

Combine 20y and 8y to get 28y.

$$8y\times 4-28y$$

Multiply 8 and 4 to get 32.

$$32y-28y$$

Combine 32y and -28y to get 4y.

$$4y$$

Expand

$$4y$$

Solution Steps

Combine 3y and -5y to get -2y.

$$\frac{\left(-2y\right)^{2}\times 2x^{2}y^{3}}{\left(-\frac{1}{2}xy^{2}\right)^{2}}-\left(20y-\left(-8y\right)\right)$$

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

$$\frac{\left(-2\right)^{2}y^{2}\times 2x^{2}y^{3}}{\left(-\frac{1}{2}xy^{2}\right)^{2}}-\left(20y-\left(-8y\right)\right)$$

Calculate -2 to the power of 2 and get 4.

$$\frac{4y^{2}\times 2x^{2}y^{3}}{\left(-\frac{1}{2}xy^{2}\right)^{2}}-\left(20y-\left(-8y\right)\right)$$

Multiply 4 and 2 to get 8.

$$\frac{8y^{2}x^{2}y^{3}}{\left(-\frac{1}{2}xy^{2}\right)^{2}}-\left(20y-\left(-8y\right)\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{8y^{5}x^{2}}{\left(-\frac{1}{2}xy^{2}\right)^{2}}-\left(20y-\left(-8y\right)\right)$$

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

$$\frac{8y^{5}x^{2}}{\left(-\frac{1}{2}\right)^{2}x^{2}\left(y^{2}\right)^{2}}-\left(20y-\left(-8y\right)\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{8y^{5}x^{2}}{\left(-\frac{1}{2}\right)^{2}x^{2}y^{4}}-\left(20y-\left(-8y\right)\right)$$

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{8y^{5}x^{2}}{\frac{1}{4}x^{2}y^{4}}-\left(20y-\left(-8y\right)\right)$$

Cancel out x^{2}y^{4} in both numerator and denominator.

$$\frac{8y}{\frac{1}{4}}-\left(20y-\left(-8y\right)\right)$$

Divide 8y by \frac{1}{4} by multiplying 8y by the reciprocal of \frac{1}{4}.

$$8y\times 4-\left(20y-\left(-8y\right)\right)$$

The opposite of -8y is 8y.

$$8y\times 4-\left(20y+8y\right)$$

Combine 20y and 8y to get 28y.

$$8y\times 4-28y$$

Multiply 8 and 4 to get 32.

$$32y-28y$$

Combine 32y and -28y to get 4y.

$$4y$$