Solve 2x^2y^2(3x^2y^2)-(-xy)(5{x}^{3}{y}^{3})-(-4{x}^{2}{y}^{2})2{x}^2{y}^2-7{x}^4{y}^4

$$2 { x }^{ 2 } { y }^{ 2 } (3 { x }^{ 2 } { y }^{ 2 } )-(-xy)(5 { x }^{ 3 } { y }^{ 3 } )-(-4 { x }^{ 2 } { y }^{ 2 } )2 { x }^{ 2 } { y }^{ 2 } -7 { x }^{ 4 } { y }^{ 4 }$$

Evaluate

$$12\left(xy\right)^{4}$$

Solution Steps

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

$$2x^{4}y^{2}\times 3y^{2}-\left(-x\right)y\times 5x^{3}y^{3}-\left(-4x^{2}y^{2}\times 2x^{2}y^{2}\right)-7x^{4}y^{4}$$

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

$$2x^{4}y^{4}\times 3-\left(-x\right)y\times 5x^{3}y^{3}-\left(-4x^{2}y^{2}\times 2x^{2}y^{2}\right)-7x^{4}y^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$2x^{4}y^{4}\times 3-\left(-x\right)y^{4}\times 5x^{3}-\left(-4x^{2}y^{2}\times 2x^{2}y^{2}\right)-7x^{4}y^{4}$$

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

$$2x^{4}y^{4}\times 3-\left(-x\right)y^{4}\times 5x^{3}-\left(-4x^{4}y^{2}\times 2y^{2}\right)-7x^{4}y^{4}$$

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

$$2x^{4}y^{4}\times 3-\left(-x\right)y^{4}\times 5x^{3}-\left(-4x^{4}y^{4}\times 2\right)-7x^{4}y^{4}$$

Multiply 2 and 3 to get 6.

$$6x^{4}y^{4}-\left(-x\right)y^{4}\times 5x^{3}-\left(-4x^{4}y^{4}\times 2\right)-7x^{4}y^{4}$$

Multiply -4 and 2 to get -8.

$$6x^{4}y^{4}-\left(-x\right)y^{4}\times 5x^{3}-\left(-8x^{4}y^{4}\right)-7x^{4}y^{4}$$

The opposite of -8x^{4}y^{4} is 8x^{4}y^{4}.

$$6x^{4}y^{4}-\left(-x\right)y^{4}\times 5x^{3}+8x^{4}y^{4}-7x^{4}y^{4}$$

Combine 8x^{4}y^{4} and -7x^{4}y^{4} to get x^{4}y^{4}.

$$6x^{4}y^{4}-\left(-x\right)y^{4}\times 5x^{3}+x^{4}y^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$6x^{4}y^{4}-\left(-x^{4}y^{4}\times 5\right)+x^{4}y^{4}$$

Multiply -1 and -1 to get 1.

$$6x^{4}y^{4}+x^{4}y^{4}\times 5+x^{4}y^{4}$$

Combine 6x^{4}y^{4} and x^{4}y^{4}\times 5 to get 11x^{4}y^{4}.

$$11x^{4}y^{4}+x^{4}y^{4}$$

Combine 11x^{4}y^{4} and x^{4}y^{4} to get 12x^{4}y^{4}.

$$12x^{4}y^{4}$$

Differentiate w.r.t. x

$$48x^{3}y^{4}$$