Solve 6(-x^2+18x-135)-(162+6x)(-2x+18)

$$6(- { x }^{ 2 } +18x-135)-(162+6x)(-2x+18)$$

Evaluate

$$6\left(x^{2}+54x-621\right)$$

Solution Steps

Use the distributive property to multiply 6 by -x^{2}+18x-135.

$$6\left(-x^{2}\right)+108x-810-\left(162+6x\right)\left(-2x+18\right)$$

Use the distributive property to multiply 162+6x by -2x+18 and combine like terms.

$$6\left(-x^{2}\right)+108x-810-\left(-216x+2916-12x^{2}\right)$$

To find the opposite of -216x+2916-12x^{2}, find the opposite of each term.

$$6\left(-x^{2}\right)+108x-810+216x-2916+12x^{2}$$

Combine 108x and 216x to get 324x.

$$6\left(-x^{2}\right)+324x-810-2916+12x^{2}$$

Subtract 2916 from -810 to get -3726.

$$6\left(-x^{2}\right)+324x-3726+12x^{2}$$

Multiply 6 and -1 to get -6.

$$-6x^{2}+324x-3726+12x^{2}$$

Combine -6x^{2} and 12x^{2} to get 6x^{2}.

$$6x^{2}+324x-3726$$

Expand

$$6x^{2}+324x-3726$$

Solution Steps

Use the distributive property to multiply 6 by -x^{2}+18x-135.

$$6\left(-x^{2}\right)+108x-810-\left(162+6x\right)\left(-2x+18\right)$$

Use the distributive property to multiply 162+6x by -2x+18 and combine like terms.

$$6\left(-x^{2}\right)+108x-810-\left(-216x+2916-12x^{2}\right)$$

To find the opposite of -216x+2916-12x^{2}, find the opposite of each term.

$$6\left(-x^{2}\right)+108x-810+216x-2916+12x^{2}$$

Combine 108x and 216x to get 324x.

$$6\left(-x^{2}\right)+324x-810-2916+12x^{2}$$

Subtract 2916 from -810 to get -3726.

$$6\left(-x^{2}\right)+324x-3726+12x^{2}$$

Multiply 6 and -1 to get -6.

$$-6x^{2}+324x-3726+12x^{2}$$

Combine -6x^{2} and 12x^{2} to get 6x^{2}.

$$6x^{2}+324x-3726$$