Solve left(3x+y-zright)left(3x-y+zright)+left(z-yright)^2

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

Evaluate

$$9x^{2}$$

Solution Steps

Use the distributive property to multiply 3x+y-z by 3x-y+z and combine like terms.

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

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(z-y\right)^{2}.

$$9x^{2}-y^{2}+2yz-z^{2}+z^{2}-2zy+y^{2}$$

Combine -z^{2} and z^{2} to get 0.

$$9x^{2}-y^{2}+2yz-2zy+y^{2}$$

Combine 2yz and -2zy to get 0.

$$9x^{2}-y^{2}+y^{2}$$

Combine -y^{2} and y^{2} to get 0.

$$9x^{2}$$

Expand

$$9x^{2}$$

Solution Steps

Use the distributive property to multiply 3x+y-z by 3x-y+z and combine like terms.

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

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(z-y\right)^{2}.

$$9x^{2}-y^{2}+2yz-z^{2}+z^{2}-2zy+y^{2}$$

Combine -z^{2} and z^{2} to get 0.

$$9x^{2}-y^{2}+2yz-2zy+y^{2}$$

Combine 2yz and -2zy to get 0.

$$9x^{2}-y^{2}+y^{2}$$

Combine -y^{2} and y^{2} to get 0.

$$9x^{2}$$