Solve (2x)^3(xy)^2+(2xy)^2(-x)^3

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

Evaluate

$$4y^{2}x^{5}$$

Solution Steps

Expand \left(2x\right)^{3}.

$$2^{3}x^{3}\left(xy\right)^{2}+\left(2xy\right)^{2}\left(-x\right)^{3}$$

Calculate 2 to the power of 3 and get 8.

$$8x^{3}\left(xy\right)^{2}+\left(2xy\right)^{2}\left(-x\right)^{3}$$

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

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

$$8x^{5}y^{2}+4x^{2}y^{2}\left(-x\right)^{3}$$

Expand \left(-x\right)^{3}.

$$8x^{5}y^{2}+4x^{2}y^{2}\left(-1\right)^{3}x^{3}$$

Calculate -1 to the power of 3 and get -1.

$$8x^{5}y^{2}+4x^{2}y^{2}\left(-1\right)x^{3}$$

Multiply 4 and -1 to get -4.

$$8x^{5}y^{2}-4x^{2}y^{2}x^{3}$$

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

$$8x^{5}y^{2}-4x^{5}y^{2}$$

Combine 8x^{5}y^{2} and -4x^{5}y^{2} to get 4x^{5}y^{2}.

$$4x^{5}y^{2}$$

Expand

$$4y^{2}x^{5}$$

Solution Steps

Expand \left(2x\right)^{3}.

$$2^{3}x^{3}\left(xy\right)^{2}+\left(2xy\right)^{2}\left(-x\right)^{3}$$

Calculate 2 to the power of 3 and get 8.

$$8x^{3}\left(xy\right)^{2}+\left(2xy\right)^{2}\left(-x\right)^{3}$$

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

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

$$8x^{5}y^{2}+4x^{2}y^{2}\left(-x\right)^{3}$$

Expand \left(-x\right)^{3}.

$$8x^{5}y^{2}+4x^{2}y^{2}\left(-1\right)^{3}x^{3}$$

Calculate -1 to the power of 3 and get -1.

$$8x^{5}y^{2}+4x^{2}y^{2}\left(-1\right)x^{3}$$

Multiply 4 and -1 to get -4.

$$8x^{5}y^{2}-4x^{2}y^{2}x^{3}$$

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

$$8x^{5}y^{2}-4x^{5}y^{2}$$

Combine 8x^{5}y^{2} and -4x^{5}y^{2} to get 4x^{5}y^{2}.

$$4x^{5}y^{2}$$