Solve 9x^{2}y^{2}z^{2}+[x^{2}z^{2}(-y)^{2}]^{2}+x^{2}(-z)^{2}(-y^{2})-(x^{2}y^{2}z^2)^2+(-2x^2)(-yz)^2

$$9 x ^ { 2 } y ^ { 2 } z ^ { 2 } + [ x ^ { 2 } z ^ { 2 } ( - y ) ^ { 2 } ] ^ { 2 } + x ^ { 2 } ( - z ) ^ { 2 } ( - y ^ { 2 } ) - ( x ^ { 2 } y ^ { 2 } z ^ { 2 } ) ^ { 2 } + ( - 2 x ^ { 2 } ) ( - y z ) ^ { 2 }$$

Evaluate

$$6\left(xyz\right)^{2}$$

Solution Steps

Calculate -y to the power of 2 and get y^{2}.

$$9x^{2}y^{2}z^{2}+\left(x^{2}z^{2}y^{2}\right)^{2}+x^{2}\left(-z\right)^{2}\left(-y^{2}\right)-\left(x^{2}y^{2}z^{2}\right)^{2}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

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

$$9x^{2}y^{2}z^{2}+\left(x^{2}\right)^{2}\left(z^{2}\right)^{2}\left(y^{2}\right)^{2}+x^{2}\left(-z\right)^{2}\left(-y^{2}\right)-\left(x^{2}y^{2}z^{2}\right)^{2}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

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

$$9x^{2}y^{2}z^{2}+x^{4}\left(z^{2}\right)^{2}\left(y^{2}\right)^{2}+x^{2}\left(-z\right)^{2}\left(-y^{2}\right)-\left(x^{2}y^{2}z^{2}\right)^{2}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

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

$$9x^{2}y^{2}z^{2}+x^{4}z^{4}\left(y^{2}\right)^{2}+x^{2}\left(-z\right)^{2}\left(-y^{2}\right)-\left(x^{2}y^{2}z^{2}\right)^{2}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

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

$$9x^{2}y^{2}z^{2}+x^{4}z^{4}y^{4}+x^{2}\left(-z\right)^{2}\left(-y^{2}\right)-\left(x^{2}y^{2}z^{2}\right)^{2}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

Calculate -z to the power of 2 and get z^{2}.

$$9x^{2}y^{2}z^{2}+x^{4}z^{4}y^{4}+x^{2}z^{2}\left(-y^{2}\right)-\left(x^{2}y^{2}z^{2}\right)^{2}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

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

$$9x^{2}y^{2}z^{2}+x^{4}z^{4}y^{4}+x^{2}z^{2}\left(-y^{2}\right)-\left(x^{2}\right)^{2}\left(y^{2}\right)^{2}\left(z^{2}\right)^{2}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

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

$$9x^{2}y^{2}z^{2}+x^{4}z^{4}y^{4}+x^{2}z^{2}\left(-y^{2}\right)-x^{4}\left(y^{2}\right)^{2}\left(z^{2}\right)^{2}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

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

$$9x^{2}y^{2}z^{2}+x^{4}z^{4}y^{4}+x^{2}z^{2}\left(-y^{2}\right)-x^{4}y^{4}\left(z^{2}\right)^{2}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

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

$$9x^{2}y^{2}z^{2}+x^{4}z^{4}y^{4}+x^{2}z^{2}\left(-y^{2}\right)-x^{4}y^{4}z^{4}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

Combine x^{4}z^{4}y^{4} and -x^{4}y^{4}z^{4} to get 0.

$$9x^{2}y^{2}z^{2}+x^{2}z^{2}\left(-y^{2}\right)-2x^{2}\left(\left(-y\right)z\right)^{2}$$

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

$$9x^{2}y^{2}z^{2}+x^{2}z^{2}\left(-y^{2}\right)-2x^{2}\left(-y\right)^{2}z^{2}$$

Calculate -y to the power of 2 and get y^{2}.

$$9x^{2}y^{2}z^{2}+x^{2}z^{2}\left(-y^{2}\right)-2x^{2}y^{2}z^{2}$$

Combine 9x^{2}y^{2}z^{2} and -2x^{2}y^{2}z^{2} to get 7x^{2}y^{2}z^{2}.

$$7x^{2}y^{2}z^{2}+x^{2}z^{2}\left(-y^{2}\right)$$

Combine 7x^{2}y^{2}z^{2} and x^{2}z^{2}\left(-1\right)y^{2} to get 6x^{2}y^{2}z^{2}.

$$6x^{2}y^{2}z^{2}$$

Expand

$$6\left(xyz\right)^{2}$$

Solution Steps

Calculate -y to the power of 2 and get y^{2}.

$$9x^{2}y^{2}z^{2}+\left(x^{2}z^{2}y^{2}\right)^{2}+x^{2}\left(-z\right)^{2}\left(-y^{2}\right)-\left(x^{2}y^{2}z^{2}\right)^{2}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

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

$$9x^{2}y^{2}z^{2}+\left(x^{2}\right)^{2}\left(z^{2}\right)^{2}\left(y^{2}\right)^{2}+x^{2}\left(-z\right)^{2}\left(-y^{2}\right)-\left(x^{2}y^{2}z^{2}\right)^{2}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

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

$$9x^{2}y^{2}z^{2}+x^{4}\left(z^{2}\right)^{2}\left(y^{2}\right)^{2}+x^{2}\left(-z\right)^{2}\left(-y^{2}\right)-\left(x^{2}y^{2}z^{2}\right)^{2}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

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

$$9x^{2}y^{2}z^{2}+x^{4}z^{4}\left(y^{2}\right)^{2}+x^{2}\left(-z\right)^{2}\left(-y^{2}\right)-\left(x^{2}y^{2}z^{2}\right)^{2}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

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

$$9x^{2}y^{2}z^{2}+x^{4}z^{4}y^{4}+x^{2}\left(-z\right)^{2}\left(-y^{2}\right)-\left(x^{2}y^{2}z^{2}\right)^{2}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

Calculate -z to the power of 2 and get z^{2}.

$$9x^{2}y^{2}z^{2}+x^{4}z^{4}y^{4}+x^{2}z^{2}\left(-y^{2}\right)-\left(x^{2}y^{2}z^{2}\right)^{2}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

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

$$9x^{2}y^{2}z^{2}+x^{4}z^{4}y^{4}+x^{2}z^{2}\left(-y^{2}\right)-\left(x^{2}\right)^{2}\left(y^{2}\right)^{2}\left(z^{2}\right)^{2}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

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

$$9x^{2}y^{2}z^{2}+x^{4}z^{4}y^{4}+x^{2}z^{2}\left(-y^{2}\right)-x^{4}\left(y^{2}\right)^{2}\left(z^{2}\right)^{2}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

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

$$9x^{2}y^{2}z^{2}+x^{4}z^{4}y^{4}+x^{2}z^{2}\left(-y^{2}\right)-x^{4}y^{4}\left(z^{2}\right)^{2}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

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

$$9x^{2}y^{2}z^{2}+x^{4}z^{4}y^{4}+x^{2}z^{2}\left(-y^{2}\right)-x^{4}y^{4}z^{4}-2x^{2}\left(\left(-y\right)z\right)^{2}$$

Combine x^{4}z^{4}y^{4} and -x^{4}y^{4}z^{4} to get 0.

$$9x^{2}y^{2}z^{2}+x^{2}z^{2}\left(-y^{2}\right)-2x^{2}\left(\left(-y\right)z\right)^{2}$$

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

$$9x^{2}y^{2}z^{2}+x^{2}z^{2}\left(-y^{2}\right)-2x^{2}\left(-y\right)^{2}z^{2}$$

Calculate -y to the power of 2 and get y^{2}.

$$9x^{2}y^{2}z^{2}+x^{2}z^{2}\left(-y^{2}\right)-2x^{2}y^{2}z^{2}$$

Combine 9x^{2}y^{2}z^{2} and -2x^{2}y^{2}z^{2} to get 7x^{2}y^{2}z^{2}.

$$7x^{2}y^{2}z^{2}+x^{2}z^{2}\left(-y^{2}\right)$$

Combine 7x^{2}y^{2}z^{2} and x^{2}z^{2}\left(-1\right)y^{2} to get 6x^{2}y^{2}z^{2}.

$$6x^{2}y^{2}z^{2}$$