Solve (4x+5)(5x-2)-(4x+5)(-2x+1)

$$( 4 x + 5 ) ( 5 x - 2 ) - ( 4 x + 5 ) ( - 2 x + 1 )$$

Evaluate

$$\left(7x-3\right)\left(4x+5\right)$$

Solution Steps

Apply the distributive property by multiplying each term of 4x+5 by each term of 5x-2.

$$20x^{2}-8x+25x-10-\left(4x+5\right)\left(-2x+1\right)$$

Combine -8x and 25x to get 17x.

$$20x^{2}+17x-10-\left(4x+5\right)\left(-2x+1\right)$$

Apply the distributive property by multiplying each term of 4x+5 by each term of -2x+1.

$$20x^{2}+17x-10-\left(-8x^{2}+4x-10x+5\right)$$

Combine 4x and -10x to get -6x.

$$20x^{2}+17x-10-\left(-8x^{2}-6x+5\right)$$

To find the opposite of -8x^{2}-6x+5, find the opposite of each term.

$$20x^{2}+17x-10-\left(-8x^{2}\right)-\left(-6x\right)-5$$

The opposite of -8x^{2} is 8x^{2}.

$$20x^{2}+17x-10+8x^{2}-\left(-6x\right)-5$$

The opposite of -6x is 6x.

$$20x^{2}+17x-10+8x^{2}+6x-5$$

Combine 20x^{2} and 8x^{2} to get 28x^{2}.

$$28x^{2}+17x-10+6x-5$$

Combine 17x and 6x to get 23x.

$$28x^{2}+23x-10-5$$

Subtract 5 from -10 to get -15.

$$28x^{2}+23x-15$$

Expand

$$28x^{2}+23x-15$$

Solution Steps

Apply the distributive property by multiplying each term of 4x+5 by each term of 5x-2.

$$20x^{2}-8x+25x-10-\left(4x+5\right)\left(-2x+1\right)$$

Combine -8x and 25x to get 17x.

$$20x^{2}+17x-10-\left(4x+5\right)\left(-2x+1\right)$$

Apply the distributive property by multiplying each term of 4x+5 by each term of -2x+1.

$$20x^{2}+17x-10-\left(-8x^{2}+4x-10x+5\right)$$

Combine 4x and -10x to get -6x.

$$20x^{2}+17x-10-\left(-8x^{2}-6x+5\right)$$

To find the opposite of -8x^{2}-6x+5, find the opposite of each term.

$$20x^{2}+17x-10-\left(-8x^{2}\right)-\left(-6x\right)-5$$

The opposite of -8x^{2} is 8x^{2}.

$$20x^{2}+17x-10+8x^{2}-\left(-6x\right)-5$$

The opposite of -6x is 6x.

$$20x^{2}+17x-10+8x^{2}+6x-5$$

Combine 20x^{2} and 8x^{2} to get 28x^{2}.

$$28x^{2}+17x-10+6x-5$$

Combine 17x and 6x to get 23x.

$$28x^{2}+23x-10-5$$

Subtract 5 from -10 to get -15.

$$28x^{2}+23x-15$$