Solve (5x+3)(7-2x)-(3x+1)(x+2)

$$(5x+3)(7-2x)-(3x+1)(x+2)$$

Evaluate

$$19+22x-13x^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 5x+3 by each term of 7-2x.

$$35x-10x^{2}+21-6x-\left(3x+1\right)\left(x+2\right)$$

Combine 35x and -6x to get 29x.

$$29x-10x^{2}+21-\left(3x+1\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of 3x+1 by each term of x+2.

$$29x-10x^{2}+21-\left(3x^{2}+6x+x+2\right)$$

Combine 6x and x to get 7x.

$$29x-10x^{2}+21-\left(3x^{2}+7x+2\right)$$

To find the opposite of 3x^{2}+7x+2, find the opposite of each term.

$$29x-10x^{2}+21-3x^{2}-7x-2$$

Combine -10x^{2} and -3x^{2} to get -13x^{2}.

$$29x-13x^{2}+21-7x-2$$

Combine 29x and -7x to get 22x.

$$22x-13x^{2}+21-2$$

Subtract 2 from 21 to get 19.

$$22x-13x^{2}+19$$

Expand

$$19+22x-13x^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 5x+3 by each term of 7-2x.

$$35x-10x^{2}+21-6x-\left(3x+1\right)\left(x+2\right)$$

Combine 35x and -6x to get 29x.

$$29x-10x^{2}+21-\left(3x+1\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of 3x+1 by each term of x+2.

$$29x-10x^{2}+21-\left(3x^{2}+6x+x+2\right)$$

Combine 6x and x to get 7x.

$$29x-10x^{2}+21-\left(3x^{2}+7x+2\right)$$

To find the opposite of 3x^{2}+7x+2, find the opposite of each term.

$$29x-10x^{2}+21-3x^{2}-7x-2$$

Combine -10x^{2} and -3x^{2} to get -13x^{2}.

$$29x-13x^{2}+21-7x-2$$

Combine 29x and -7x to get 22x.

$$22x-13x^{2}+21-2$$

Subtract 2 from 21 to get 19.

$$22x-13x^{2}+19$$