Solve left(-3xy^2z^4right)^2+x^2{y}^{4}{z}^{8}-x{y}^{2}{z}^{3}x{y}^{2}{z}^5-10{x}^2{y}^4{z}^8

$${ \left(-3x { y }^{ 2 } { z }^{ 4 } \right) }^{ 2 } + { x }^{ 2 } { y }^{ 4 } { z }^{ 8 } -x { y }^{ 2 } { z }^{ 3 } x { y }^{ 2 } { z }^{ 5 } -10 { x }^{ 2 } { y }^{ 4 } { z }^{ 8 }$$

Evaluate

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

Solution Steps

Multiply x and x to get x^{2}.

$$\left(-3xy^{2}z^{4}\right)^{2}+x^{2}y^{4}z^{8}-x^{2}y^{2}z^{3}y^{2}z^{5}-10x^{2}y^{4}z^{8}$$

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

$$\left(-3xy^{2}z^{4}\right)^{2}+x^{2}y^{4}z^{8}-x^{2}y^{4}z^{3}z^{5}-10x^{2}y^{4}z^{8}$$

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\left(-3xy^{2}z^{4}\right)^{2}+x^{2}y^{4}z^{8}-x^{2}y^{4}z^{8}-10x^{2}y^{4}z^{8}$$

Expand \left(-3xy^{2}z^{4}\right)^{2}.

$$\left(-3\right)^{2}x^{2}\left(y^{2}\right)^{2}\left(z^{4}\right)^{2}+x^{2}y^{4}z^{8}-x^{2}y^{4}z^{8}-10x^{2}y^{4}z^{8}$$

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

$$\left(-3\right)^{2}x^{2}y^{4}\left(z^{4}\right)^{2}+x^{2}y^{4}z^{8}-x^{2}y^{4}z^{8}-10x^{2}y^{4}z^{8}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\left(-3\right)^{2}x^{2}y^{4}z^{8}+x^{2}y^{4}z^{8}-x^{2}y^{4}z^{8}-10x^{2}y^{4}z^{8}$$

Calculate -3 to the power of 2 and get 9.

$$9x^{2}y^{4}z^{8}+x^{2}y^{4}z^{8}-x^{2}y^{4}z^{8}-10x^{2}y^{4}z^{8}$$

Combine 9x^{2}y^{4}z^{8} and x^{2}y^{4}z^{8} to get 10x^{2}y^{4}z^{8}.

$$10x^{2}y^{4}z^{8}-x^{2}y^{4}z^{8}-10x^{2}y^{4}z^{8}$$

Combine 10x^{2}y^{4}z^{8} and -x^{2}y^{4}z^{8} to get 9x^{2}y^{4}z^{8}.

$$9x^{2}y^{4}z^{8}-10x^{2}y^{4}z^{8}$$

Combine 9x^{2}y^{4}z^{8} and -10x^{2}y^{4}z^{8} to get -x^{2}y^{4}z^{8}.

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

Expand

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

Solution Steps

Multiply x and x to get x^{2}.

$$\left(-3xy^{2}z^{4}\right)^{2}+x^{2}y^{4}z^{8}-x^{2}y^{2}z^{3}y^{2}z^{5}-10x^{2}y^{4}z^{8}$$

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

$$\left(-3xy^{2}z^{4}\right)^{2}+x^{2}y^{4}z^{8}-x^{2}y^{4}z^{3}z^{5}-10x^{2}y^{4}z^{8}$$

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\left(-3xy^{2}z^{4}\right)^{2}+x^{2}y^{4}z^{8}-x^{2}y^{4}z^{8}-10x^{2}y^{4}z^{8}$$

Expand \left(-3xy^{2}z^{4}\right)^{2}.

$$\left(-3\right)^{2}x^{2}\left(y^{2}\right)^{2}\left(z^{4}\right)^{2}+x^{2}y^{4}z^{8}-x^{2}y^{4}z^{8}-10x^{2}y^{4}z^{8}$$

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

$$\left(-3\right)^{2}x^{2}y^{4}\left(z^{4}\right)^{2}+x^{2}y^{4}z^{8}-x^{2}y^{4}z^{8}-10x^{2}y^{4}z^{8}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\left(-3\right)^{2}x^{2}y^{4}z^{8}+x^{2}y^{4}z^{8}-x^{2}y^{4}z^{8}-10x^{2}y^{4}z^{8}$$

Calculate -3 to the power of 2 and get 9.

$$9x^{2}y^{4}z^{8}+x^{2}y^{4}z^{8}-x^{2}y^{4}z^{8}-10x^{2}y^{4}z^{8}$$

Combine 9x^{2}y^{4}z^{8} and x^{2}y^{4}z^{8} to get 10x^{2}y^{4}z^{8}.

$$10x^{2}y^{4}z^{8}-x^{2}y^{4}z^{8}-10x^{2}y^{4}z^{8}$$

Combine 10x^{2}y^{4}z^{8} and -x^{2}y^{4}z^{8} to get 9x^{2}y^{4}z^{8}.

$$9x^{2}y^{4}z^{8}-10x^{2}y^{4}z^{8}$$

Combine 9x^{2}y^{4}z^{8} and -10x^{2}y^{4}z^{8} to get -x^{2}y^{4}z^{8}.

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