Solve z^2+5(x-z)^2

$$z ^ { 2 } + 5 ( x - z ) ^ { 2 }$$

Evaluate

$$5\left(x-z\right)^{2}+z^{2}$$

Solution Steps

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

$$z^{2}+5\left(x^{2}-2xz+z^{2}\right)$$

Use the distributive property to multiply 5 by x^{2}-2xz+z^{2}.

$$z^{2}+5x^{2}-10xz+5z^{2}$$

Combine z^{2} and 5z^{2} to get 6z^{2}.

$$6z^{2}+5x^{2}-10xz$$

Expand

$$5x^{2}-10xz+6z^{2}$$

Solution Steps

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

$$z^{2}+5\left(x^{2}-2xz+z^{2}\right)$$

Use the distributive property to multiply 5 by x^{2}-2xz+z^{2}.

$$z^{2}+5x^{2}-10xz+5z^{2}$$

Combine z^{2} and 5z^{2} to get 6z^{2}.

$$6z^{2}+5x^{2}-10xz$$