Solve bleft(b+3right)left(b-4right)-left(2b-7right)left(b+3right)+b^2-4

$$b \left( b+3 \right) \left( b-4 \right) - \left( 2b-7 \right) \left( b+3 \right) + { b }^{ 2 } -4$$

Evaluate

$$b^{3}-2b^{2}-11b+17$$

Solution Steps

Use the distributive property to multiply b by b+3.

$$\left(b^{2}+3b\right)\left(b-4\right)-\left(2b-7\right)\left(b+3\right)+b^{2}-4$$

Use the distributive property to multiply b^{2}+3b by b-4 and combine like terms.

$$b^{3}-b^{2}-12b-\left(2b-7\right)\left(b+3\right)+b^{2}-4$$

Use the distributive property to multiply 2b-7 by b+3 and combine like terms.

$$b^{3}-b^{2}-12b-\left(2b^{2}-b-21\right)+b^{2}-4$$

To find the opposite of 2b^{2}-b-21, find the opposite of each term.

$$b^{3}-b^{2}-12b-2b^{2}+b+21+b^{2}-4$$

Combine -b^{2} and -2b^{2} to get -3b^{2}.

$$b^{3}-3b^{2}-12b+b+21+b^{2}-4$$

Combine -12b and b to get -11b.

$$b^{3}-3b^{2}-11b+21+b^{2}-4$$

Combine -3b^{2} and b^{2} to get -2b^{2}.

$$b^{3}-2b^{2}-11b+21-4$$

Subtract 4 from 21 to get 17.

$$b^{3}-2b^{2}-11b+17$$

Expand

$$b^{3}-2b^{2}-11b+17$$

Solution Steps

Use the distributive property to multiply b by b+3.

$$\left(b^{2}+3b\right)\left(b-4\right)-\left(2b-7\right)\left(b+3\right)+b^{2}-4$$

Use the distributive property to multiply b^{2}+3b by b-4 and combine like terms.

$$b^{3}-b^{2}-12b-\left(2b-7\right)\left(b+3\right)+b^{2}-4$$

Use the distributive property to multiply 2b-7 by b+3 and combine like terms.

$$b^{3}-b^{2}-12b-\left(2b^{2}-b-21\right)+b^{2}-4$$

To find the opposite of 2b^{2}-b-21, find the opposite of each term.

$$b^{3}-b^{2}-12b-2b^{2}+b+21+b^{2}-4$$

Combine -b^{2} and -2b^{2} to get -3b^{2}.

$$b^{3}-3b^{2}-12b+b+21+b^{2}-4$$

Combine -12b and b to get -11b.

$$b^{3}-3b^{2}-11b+21+b^{2}-4$$

Combine -3b^{2} and b^{2} to get -2b^{2}.

$$b^{3}-2b^{2}-11b+21-4$$

Subtract 4 from 21 to get 17.

$$b^{3}-2b^{2}-11b+17$$