Solve (7xy^{3}-2xy^3-4xy^3)*(2x)^2+(-xy)^3

$$( 7 x y ^ { 3 } - 2 x y ^ { 3 } - 4 x y ^ { 3 } ) \cdot ( 2 x ) ^ { 2 } + ( - x y ) ^ { 3 }$$

Evaluate

$$3\left(xy\right)^{3}$$

Solution Steps

Combine 7xy^{3} and -2xy^{3} to get 5xy^{3}.

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

Combine 5xy^{3} and -4xy^{3} to get xy^{3}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$x^{3}y^{3}\times 4+\left(\left(-x\right)y\right)^{3}$$

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

$$x^{3}y^{3}\times 4+\left(-x\right)^{3}y^{3}$$

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

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

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

$$x^{3}y^{3}\times 4-x^{3}y^{3}$$

Combine x^{3}y^{3}\times 4 and -x^{3}y^{3} to get 3x^{3}y^{3}.

$$3x^{3}y^{3}$$

Expand

$$3\left(xy\right)^{3}$$

Solution Steps

Combine 7xy^{3} and -2xy^{3} to get 5xy^{3}.

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

Combine 5xy^{3} and -4xy^{3} to get xy^{3}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$x^{3}y^{3}\times 4+\left(\left(-x\right)y\right)^{3}$$

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

$$x^{3}y^{3}\times 4+\left(-x\right)^{3}y^{3}$$

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

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

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

$$x^{3}y^{3}\times 4-x^{3}y^{3}$$

Combine x^{3}y^{3}\times 4 and -x^{3}y^{3} to get 3x^{3}y^{3}.

$$3x^{3}y^{3}$$