Solve (b-2)*(b+3)-(b+1)*(b-3)

$$( b - 2 ) \cdot ( b + 3 ) - ( b + 1 ) \cdot ( b - 3 )$$

Evaluate

$$3\left(b-1\right)$$

Solution Steps

Apply the distributive property by multiplying each term of b-2 by each term of b+3.

$$b^{2}+3b-2b-6-\left(b+1\right)\left(b-3\right)$$

Combine 3b and -2b to get b.

$$b^{2}+b-6-\left(b+1\right)\left(b-3\right)$$

Apply the distributive property by multiplying each term of b+1 by each term of b-3.

$$b^{2}+b-6-\left(b^{2}-3b+b-3\right)$$

Combine -3b and b to get -2b.

$$b^{2}+b-6-\left(b^{2}-2b-3\right)$$

To find the opposite of b^{2}-2b-3, find the opposite of each term.

$$b^{2}+b-6-b^{2}-\left(-2b\right)-\left(-3\right)$$

The opposite of -2b is 2b.

$$b^{2}+b-6-b^{2}+2b-\left(-3\right)$$

The opposite of -3 is 3.

$$b^{2}+b-6-b^{2}+2b+3$$

Combine b^{2} and -b^{2} to get 0.

$$b-6+2b+3$$

Combine b and 2b to get 3b.

$$3b-6+3$$

Add -6 and 3 to get -3.

$$3b-3$$

Expand

$$3b-3$$

Solution Steps

Apply the distributive property by multiplying each term of b-2 by each term of b+3.

$$b^{2}+3b-2b-6-\left(b+1\right)\left(b-3\right)$$

Combine 3b and -2b to get b.

$$b^{2}+b-6-\left(b+1\right)\left(b-3\right)$$

Apply the distributive property by multiplying each term of b+1 by each term of b-3.

$$b^{2}+b-6-\left(b^{2}-3b+b-3\right)$$

Combine -3b and b to get -2b.

$$b^{2}+b-6-\left(b^{2}-2b-3\right)$$

To find the opposite of b^{2}-2b-3, find the opposite of each term.

$$b^{2}+b-6-b^{2}-\left(-2b\right)-\left(-3\right)$$

The opposite of -2b is 2b.

$$b^{2}+b-6-b^{2}+2b-\left(-3\right)$$

The opposite of -3 is 3.

$$b^{2}+b-6-b^{2}+2b+3$$

Combine b^{2} and -b^{2} to get 0.

$$b-6+2b+3$$

Combine b and 2b to get 3b.

$$3b-6+3$$

Add -6 and 3 to get -3.

$$3b-3$$