Solve 5[(6-z)^2-5]

$$5 [ ( 6 - z ) ^ { 2 } - 5 ]$$

Expand

$$5z^{2}-60z+155$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6-z\right)^{2}.

$$5\left(36-12z+z^{2}-5\right)$$

Subtract 5 from 36 to get 31.

$$5\left(31-12z+z^{2}\right)$$

Use the distributive property to multiply 5 by 31-12z+z^{2}.

$$155-60z+5z^{2}$$

Evaluate

$$5\left(\left(6-z\right)^{2}-5\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6-z\right)^{2}.

$$5\left(36-12z+z^{2}-5\right)$$

Subtract 5 from 36 to get 31.

$$5\left(31-12z+z^{2}\right)$$

Use the distributive property to multiply 5 by 31-12z+z^{2}.

$$155-60z+5z^{2}$$