Solve {l}{5x(2x-4)-3(2x^2+8)}{-3(2m-6)-(8-6m)}

$$\left. \begin{array} { l } { 5 x ( 2 x - 4 ) - 3 ( 2 x ^ { 2 } + 8 ) } \\ { - 3 ( 2 m - 6 ) - ( 8 - 6 m ) } \end{array} \right.$$

Evaluate

$$4x^{2}-20x-14$$

Solution Steps

Use the distributive property to multiply 5x by 2x-4.

$$10x^{2}-20x-3\left(2x^{2}+8\right)-3\left(2m-6\right)-\left(8-6m\right)$$

Use the distributive property to multiply -3 by 2x^{2}+8.

$$10x^{2}-20x-6x^{2}-24-3\left(2m-6\right)-\left(8-6m\right)$$

Combine 10x^{2} and -6x^{2} to get 4x^{2}.

$$4x^{2}-20x-24-3\left(2m-6\right)-\left(8-6m\right)$$

Use the distributive property to multiply -3 by 2m-6.

$$4x^{2}-20x-24-6m+18-\left(8-6m\right)$$

Add -24 and 18 to get -6.

$$4x^{2}-20x-6-6m-\left(8-6m\right)$$

To find the opposite of 8-6m, find the opposite of each term.

$$4x^{2}-20x-6-6m-8+6m$$

Subtract 8 from -6 to get -14.

$$4x^{2}-20x-14-6m+6m$$

Combine -6m and 6m to get 0.

$$4x^{2}-20x-14$$

Expand

$$4x^{2}-20x-14$$

Solution Steps

Use the distributive property to multiply 5x by 2x-4.

$$10x^{2}-20x-3\left(2x^{2}+8\right)-3\left(2m-6\right)-\left(8-6m\right)$$

Use the distributive property to multiply -3 by 2x^{2}+8.

$$10x^{2}-20x-6x^{2}-24-3\left(2m-6\right)-\left(8-6m\right)$$

Combine 10x^{2} and -6x^{2} to get 4x^{2}.

$$4x^{2}-20x-24-3\left(2m-6\right)-\left(8-6m\right)$$

Use the distributive property to multiply -3 by 2m-6.

$$4x^{2}-20x-24-6m+18-\left(8-6m\right)$$

Add -24 and 18 to get -6.

$$4x^{2}-20x-6-6m-\left(8-6m\right)$$

To find the opposite of 8-6m, find the opposite of each term.

$$4x^{2}-20x-6-6m-8+6m$$

Subtract 8 from -6 to get -14.

$$4x^{2}-20x-14-6m+6m$$

Combine -6m and 6m to get 0.

$$4x^{2}-20x-14$$