Solve (8)(x+3)(x+4)-x(x+2)-5

$$( 8 ) ( x + 3 ) ( x + 4 ) - x ( x + 2 ) - 5$$

Evaluate

$$7x^{2}+54x+91$$

Solution Steps

Use the distributive property to multiply 8 by x+3.

$$\left(8x+24\right)\left(x+4\right)-x\left(x+2\right)-5$$

Apply the distributive property by multiplying each term of 8x+24 by each term of x+4.

$$8x^{2}+32x+24x+96-x\left(x+2\right)-5$$

Combine 32x and 24x to get 56x.

$$8x^{2}+56x+96-x\left(x+2\right)-5$$

Use the distributive property to multiply x by x+2.

$$8x^{2}+56x+96-\left(x^{2}+2x\right)-5$$

To find the opposite of x^{2}+2x, find the opposite of each term.

$$8x^{2}+56x+96-x^{2}-2x-5$$

Combine 8x^{2} and -x^{2} to get 7x^{2}.

$$7x^{2}+56x+96-2x-5$$

Combine 56x and -2x to get 54x.

$$7x^{2}+54x+96-5$$

Subtract 5 from 96 to get 91.

$$7x^{2}+54x+91$$

Expand

$$7x^{2}+54x+91$$

Solution Steps

Use the distributive property to multiply 8 by x+3.

$$\left(8x+24\right)\left(x+4\right)-x\left(x+2\right)-5$$

Apply the distributive property by multiplying each term of 8x+24 by each term of x+4.

$$8x^{2}+32x+24x+96-x\left(x+2\right)-5$$

Combine 32x and 24x to get 56x.

$$8x^{2}+56x+96-x\left(x+2\right)-5$$

Use the distributive property to multiply x by x+2.

$$8x^{2}+56x+96-\left(x^{2}+2x\right)-5$$

To find the opposite of x^{2}+2x, find the opposite of each term.

$$8x^{2}+56x+96-x^{2}-2x-5$$

Combine 8x^{2} and -x^{2} to get 7x^{2}.

$$7x^{2}+56x+96-2x-5$$

Combine 56x and -2x to get 54x.

$$7x^{2}+54x+96-5$$

Subtract 5 from 96 to get 91.

$$7x^{2}+54x+91$$