Solve -(x-3)(x+8)-left(x+2right)^2

$$-(x-3)(x+8)- { \left(x+2 \right) }^{ 2 }$$

Evaluate

$$20-9x-2x^{2}$$

Solution Steps

To find the opposite of x-3, find the opposite of each term.

$$\left(-x+3\right)\left(x+8\right)-\left(x+2\right)^{2}$$

Use the distributive property to multiply -x+3 by x+8 and combine like terms.

$$-x^{2}-5x+24-\left(x+2\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.

$$-x^{2}-5x+24-\left(x^{2}+4x+4\right)$$

To find the opposite of x^{2}+4x+4, find the opposite of each term.

$$-x^{2}-5x+24-x^{2}-4x-4$$

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

$$-2x^{2}-5x+24-4x-4$$

Combine -5x and -4x to get -9x.

$$-2x^{2}-9x+24-4$$

Subtract 4 from 24 to get 20.

$$-2x^{2}-9x+20$$

Expand

$$20-9x-2x^{2}$$

Solution Steps

To find the opposite of x-3, find the opposite of each term.

$$\left(-x+3\right)\left(x+8\right)-\left(x+2\right)^{2}$$

Use the distributive property to multiply -x+3 by x+8 and combine like terms.

$$-x^{2}-5x+24-\left(x+2\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.

$$-x^{2}-5x+24-\left(x^{2}+4x+4\right)$$

To find the opposite of x^{2}+4x+4, find the opposite of each term.

$$-x^{2}-5x+24-x^{2}-4x-4$$

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

$$-2x^{2}-5x+24-4x-4$$

Combine -5x and -4x to get -9x.

$$-2x^{2}-9x+24-4$$

Subtract 4 from 24 to get 20.

$$-2x^{2}-9x+20$$