Solve {l}{5x(x-8)+(x+2)(x-1)}{-3(-4x+3)-(x-2)}

$$\left. \begin{array} { l } { 5 x ( x - 8 ) + ( x + 2 ) ( x - 1 ) } \\ { - 3 ( - 4 x + 3 ) - ( x - 2 ) } \end{array} \right.$$

Evaluate

$$6x^{2}-28x-9$$

Solution Steps

Use the distributive property to multiply 5x by x-8.

$$5x^{2}-40x+\left(x+2\right)\left(x-1\right)-3\left(-4x+3\right)-\left(x-2\right)$$

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

$$5x^{2}-40x+x^{2}-x+2x-2-3\left(-4x+3\right)-\left(x-2\right)$$

Combine -x and 2x to get x.

$$5x^{2}-40x+x^{2}+x-2-3\left(-4x+3\right)-\left(x-2\right)$$

Combine 5x^{2} and x^{2} to get 6x^{2}.

$$6x^{2}-40x+x-2-3\left(-4x+3\right)-\left(x-2\right)$$

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

$$6x^{2}-39x-2-3\left(-4x+3\right)-\left(x-2\right)$$

Use the distributive property to multiply -3 by -4x+3.

$$6x^{2}-39x-2+12x-9-\left(x-2\right)$$

Combine -39x and 12x to get -27x.

$$6x^{2}-27x-2-9-\left(x-2\right)$$

Subtract 9 from -2 to get -11.

$$6x^{2}-27x-11-\left(x-2\right)$$

To find the opposite of x-2, find the opposite of each term.

$$6x^{2}-27x-11-x-\left(-2\right)$$

The opposite of -2 is 2.

$$6x^{2}-27x-11-x+2$$

Combine -27x and -x to get -28x.

$$6x^{2}-28x-11+2$$

Add -11 and 2 to get -9.

$$6x^{2}-28x-9$$

Expand

$$6x^{2}-28x-9$$

Solution Steps

Use the distributive property to multiply 5x by x-8.

$$5x^{2}-40x+\left(x+2\right)\left(x-1\right)-3\left(-4x+3\right)-\left(x-2\right)$$

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

$$5x^{2}-40x+x^{2}-x+2x-2-3\left(-4x+3\right)-\left(x-2\right)$$

Combine -x and 2x to get x.

$$5x^{2}-40x+x^{2}+x-2-3\left(-4x+3\right)-\left(x-2\right)$$

Combine 5x^{2} and x^{2} to get 6x^{2}.

$$6x^{2}-40x+x-2-3\left(-4x+3\right)-\left(x-2\right)$$

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

$$6x^{2}-39x-2-3\left(-4x+3\right)-\left(x-2\right)$$

Use the distributive property to multiply -3 by -4x+3.

$$6x^{2}-39x-2+12x-9-\left(x-2\right)$$

Combine -39x and 12x to get -27x.

$$6x^{2}-27x-2-9-\left(x-2\right)$$

Subtract 9 from -2 to get -11.

$$6x^{2}-27x-11-\left(x-2\right)$$

To find the opposite of x-2, find the opposite of each term.

$$6x^{2}-27x-11-x-\left(-2\right)$$

The opposite of -2 is 2.

$$6x^{2}-27x-11-x+2$$

Combine -27x and -x to get -28x.

$$6x^{2}-28x-11+2$$

Add -11 and 2 to get -9.

$$6x^{2}-28x-9$$