Solve z^2+6(y-z)^2

$$z ^ { 2 } + 6 ( y - z ) ^ { 2 }$$

Evaluate

$$6\left(y-z\right)^{2}+z^{2}$$

Solution Steps

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

$$z^{2}+6\left(y^{2}-2yz+z^{2}\right)$$

Use the distributive property to multiply 6 by y^{2}-2yz+z^{2}.

$$z^{2}+6y^{2}-12yz+6z^{2}$$

Combine z^{2} and 6z^{2} to get 7z^{2}.

$$7z^{2}+6y^{2}-12yz$$

Expand

$$6y^{2}-12yz+7z^{2}$$

Solution Steps

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

$$z^{2}+6\left(y^{2}-2yz+z^{2}\right)$$

Use the distributive property to multiply 6 by y^{2}-2yz+z^{2}.

$$z^{2}+6y^{2}-12yz+6z^{2}$$

Combine z^{2} and 6z^{2} to get 7z^{2}.

$$7z^{2}+6y^{2}-12yz$$