Solve 17(a+1)-4(a+1)^2

$$17 ( a + 1 ) - 4 ( a + 1 ) ^ { 2 }$$

Evaluate

$$\left(13-4a\right)\left(a+1\right)$$

Solution Steps

Use the distributive property to multiply 17 by a+1.

$$17a+17-4\left(a+1\right)^{2}$$

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

$$17a+17-4\left(a^{2}+2a+1\right)$$

Use the distributive property to multiply -4 by a^{2}+2a+1.

$$17a+17-4a^{2}-8a-4$$

Combine 17a and -8a to get 9a.

$$9a+17-4a^{2}-4$$

Subtract 4 from 17 to get 13.

$$9a+13-4a^{2}$$

Expand

$$13+9a-4a^{2}$$

Solution Steps

Use the distributive property to multiply 17 by a+1.

$$17a+17-4\left(a+1\right)^{2}$$

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

$$17a+17-4\left(a^{2}+2a+1\right)$$

Use the distributive property to multiply -4 by a^{2}+2a+1.

$$17a+17-4a^{2}-8a-4$$

Combine 17a and -8a to get 9a.

$$9a+17-4a^{2}-4$$

Subtract 4 from 17 to get 13.

$$9a+13-4a^{2}$$