Solve z^2+3(x-z)^2

$$z ^ { 2 } + 3 ( x - z ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

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

Use the distributive property to multiply 3 by x^{2}-2xz+z^{2}.

$$z^{2}+3x^{2}-6xz+3z^{2}$$

Combine z^{2} and 3z^{2} to get 4z^{2}.

$$4z^{2}+3x^{2}-6xz$$

Expand

$$3x^{2}-6xz+4z^{2}$$

Solution Steps

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

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

Use the distributive property to multiply 3 by x^{2}-2xz+z^{2}.

$$z^{2}+3x^{2}-6xz+3z^{2}$$

Combine z^{2} and 3z^{2} to get 4z^{2}.

$$4z^{2}+3x^{2}-6xz$$