Solve =(2-5x)(3x-1)-(4-10x)(4x+3)

$$= ( 2 - 5 x ) ( 3 x - 1 ) - ( 4 - 10 x ) ( 4 x + 3 )$$

Evaluate

$$25x^{2}+25x-14$$

Solution Steps

Apply the distributive property by multiplying each term of 2-5x by each term of 3x-1.

$$6x-2-15x^{2}+5x-\left(4-10x\right)\left(4x+3\right)$$

Combine 6x and 5x to get 11x.

$$11x-2-15x^{2}-\left(4-10x\right)\left(4x+3\right)$$

Apply the distributive property by multiplying each term of 4-10x by each term of 4x+3.

$$11x-2-15x^{2}-\left(16x+12-40x^{2}-30x\right)$$

Combine 16x and -30x to get -14x.

$$11x-2-15x^{2}-\left(-14x+12-40x^{2}\right)$$

To find the opposite of -14x+12-40x^{2}, find the opposite of each term.

$$11x-2-15x^{2}-\left(-14x\right)-12-\left(-40x^{2}\right)$$

The opposite of -14x is 14x.

$$11x-2-15x^{2}+14x-12-\left(-40x^{2}\right)$$

The opposite of -40x^{2} is 40x^{2}.

$$11x-2-15x^{2}+14x-12+40x^{2}$$

Combine 11x and 14x to get 25x.

$$25x-2-15x^{2}-12+40x^{2}$$

Subtract 12 from -2 to get -14.

$$25x-14-15x^{2}+40x^{2}$$

Combine -15x^{2} and 40x^{2} to get 25x^{2}.

$$25x-14+25x^{2}$$

Expand

$$25x^{2}+25x-14$$

Solution Steps

Apply the distributive property by multiplying each term of 2-5x by each term of 3x-1.

$$6x-2-15x^{2}+5x-\left(4-10x\right)\left(4x+3\right)$$

Combine 6x and 5x to get 11x.

$$11x-2-15x^{2}-\left(4-10x\right)\left(4x+3\right)$$

Apply the distributive property by multiplying each term of 4-10x by each term of 4x+3.

$$11x-2-15x^{2}-\left(16x+12-40x^{2}-30x\right)$$

Combine 16x and -30x to get -14x.

$$11x-2-15x^{2}-\left(-14x+12-40x^{2}\right)$$

To find the opposite of -14x+12-40x^{2}, find the opposite of each term.

$$11x-2-15x^{2}-\left(-14x\right)-12-\left(-40x^{2}\right)$$

The opposite of -14x is 14x.

$$11x-2-15x^{2}+14x-12-\left(-40x^{2}\right)$$

The opposite of -40x^{2} is 40x^{2}.

$$11x-2-15x^{2}+14x-12+40x^{2}$$

Combine 11x and 14x to get 25x.

$$25x-2-15x^{2}-12+40x^{2}$$

Subtract 12 from -2 to get -14.

$$25x-14-15x^{2}+40x^{2}$$

Combine -15x^{2} and 40x^{2} to get 25x^{2}.

$$25x-14+25x^{2}$$