Solve (5)x^2*(2xy)^2-(-x^2y)^2

$$( 5 ) x ^ { 2 } \cdot ( 2 x y ) ^ { 2 } - ( - x ^ { 2 } y ) ^ { 2 }$$

Evaluate

$$19y^{2}x^{4}$$

Solution Steps

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

$$5x^{2}\times 2^{2}x^{2}y^{2}-\left(\left(-x^{2}\right)y\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$5x^{2}\times 4x^{2}y^{2}-\left(\left(-x^{2}\right)y\right)^{2}$$

Multiply 5 and 4 to get 20.

$$20x^{2}x^{2}y^{2}-\left(\left(-x^{2}\right)y\right)^{2}$$

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

$$20x^{4}y^{2}-\left(\left(-x^{2}\right)y\right)^{2}$$

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

$$20x^{4}y^{2}-\left(-x^{2}\right)^{2}y^{2}$$

Calculate -x^{2} to the power of 2 and get \left(x^{2}\right)^{2}.

$$20x^{4}y^{2}-\left(x^{2}\right)^{2}y^{2}$$

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

$$20x^{4}y^{2}-x^{4}y^{2}$$

Combine 20x^{4}y^{2} and -x^{4}y^{2} to get 19x^{4}y^{2}.

$$19x^{4}y^{2}$$

Expand

$$19y^{2}x^{4}$$

Solution Steps

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

$$5x^{2}\times 2^{2}x^{2}y^{2}-\left(\left(-x^{2}\right)y\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$5x^{2}\times 4x^{2}y^{2}-\left(\left(-x^{2}\right)y\right)^{2}$$

Multiply 5 and 4 to get 20.

$$20x^{2}x^{2}y^{2}-\left(\left(-x^{2}\right)y\right)^{2}$$

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

$$20x^{4}y^{2}-\left(\left(-x^{2}\right)y\right)^{2}$$

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

$$20x^{4}y^{2}-\left(-x^{2}\right)^{2}y^{2}$$

Calculate -x^{2} to the power of 2 and get \left(x^{2}\right)^{2}.

$$20x^{4}y^{2}-\left(x^{2}\right)^{2}y^{2}$$

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

$$20x^{4}y^{2}-x^{4}y^{2}$$

Combine 20x^{4}y^{2} and -x^{4}y^{2} to get 19x^{4}y^{2}.

$$19x^{4}y^{2}$$