Solve (5x-3)(7x+2)-(5x+1)(x-8)

$$(5x-3)(7x+2)-(5x+1)(x-8)$$

Evaluate

$$30x^{2}+28x+2$$

Solution Steps

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

$$35x^{2}+10x-21x-6-\left(5x+1\right)\left(x-8\right)$$

Combine 10x and -21x to get -11x.

$$35x^{2}-11x-6-\left(5x+1\right)\left(x-8\right)$$

Apply the distributive property by multiplying each term of 5x+1 by each term of x-8.

$$35x^{2}-11x-6-\left(5x^{2}-40x+x-8\right)$$

Combine -40x and x to get -39x.

$$35x^{2}-11x-6-\left(5x^{2}-39x-8\right)$$

To find the opposite of 5x^{2}-39x-8, find the opposite of each term.

$$35x^{2}-11x-6-5x^{2}-\left(-39x\right)-\left(-8\right)$$

The opposite of -39x is 39x.

$$35x^{2}-11x-6-5x^{2}+39x-\left(-8\right)$$

The opposite of -8 is 8.

$$35x^{2}-11x-6-5x^{2}+39x+8$$

Combine 35x^{2} and -5x^{2} to get 30x^{2}.

$$30x^{2}-11x-6+39x+8$$

Combine -11x and 39x to get 28x.

$$30x^{2}+28x-6+8$$

Add -6 and 8 to get 2.

$$30x^{2}+28x+2$$

Expand

$$30x^{2}+28x+2$$

Solution Steps

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

$$35x^{2}+10x-21x-6-\left(5x+1\right)\left(x-8\right)$$

Combine 10x and -21x to get -11x.

$$35x^{2}-11x-6-\left(5x+1\right)\left(x-8\right)$$

Apply the distributive property by multiplying each term of 5x+1 by each term of x-8.

$$35x^{2}-11x-6-\left(5x^{2}-40x+x-8\right)$$

Combine -40x and x to get -39x.

$$35x^{2}-11x-6-\left(5x^{2}-39x-8\right)$$

To find the opposite of 5x^{2}-39x-8, find the opposite of each term.

$$35x^{2}-11x-6-5x^{2}-\left(-39x\right)-\left(-8\right)$$

The opposite of -39x is 39x.

$$35x^{2}-11x-6-5x^{2}+39x-\left(-8\right)$$

The opposite of -8 is 8.

$$35x^{2}-11x-6-5x^{2}+39x+8$$

Combine 35x^{2} and -5x^{2} to get 30x^{2}.

$$30x^{2}-11x-6+39x+8$$

Combine -11x and 39x to get 28x.

$$30x^{2}+28x-6+8$$

Add -6 and 8 to get 2.

$$30x^{2}+28x+2$$