Solve 5(a-1)^2-6(a-1)+2

$$5 ( a - 1 ) ^ { 2 } - 6 ( a - 1 ) + 2$$

Evaluate

$$5a^{2}-16a+13$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-1\right)^{2}.

$$5\left(a^{2}-2a+1\right)-6\left(a-1\right)+2$$

Use the distributive property to multiply 5 by a^{2}-2a+1.

$$5a^{2}-10a+5-6\left(a-1\right)+2$$

Use the distributive property to multiply -6 by a-1.

$$5a^{2}-10a+5-6a+6+2$$

Combine -10a and -6a to get -16a.

$$5a^{2}-16a+5+6+2$$

Add 5 and 6 to get 11.

$$5a^{2}-16a+11+2$$

Add 11 and 2 to get 13.

$$5a^{2}-16a+13$$

Expand

$$5a^{2}-16a+13$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-1\right)^{2}.

$$5\left(a^{2}-2a+1\right)-6\left(a-1\right)+2$$

Use the distributive property to multiply 5 by a^{2}-2a+1.

$$5a^{2}-10a+5-6\left(a-1\right)+2$$

Use the distributive property to multiply -6 by a-1.

$$5a^{2}-10a+5-6a+6+2$$

Combine -10a and -6a to get -16a.

$$5a^{2}-16a+5+6+2$$

Add 5 and 6 to get 11.

$$5a^{2}-16a+11+2$$

Add 11 and 2 to get 13.

$$5a^{2}-16a+13$$