Solve -2left(x-2right)^2-3left(x-2right)+5

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

Evaluate

$$\left(3-x\right)\left(2x+1\right)$$

Solution Steps

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

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

Use the distributive property to multiply -2 by x^{2}-4x+4.

$$-2x^{2}+8x-8-3\left(x-2\right)+5$$

Use the distributive property to multiply -3 by x-2.

$$-2x^{2}+8x-8-3x+6+5$$

Combine 8x and -3x to get 5x.

$$-2x^{2}+5x-8+6+5$$

Add -8 and 6 to get -2.

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

Add -2 and 5 to get 3.

$$-2x^{2}+5x+3$$

Expand

$$3+5x-2x^{2}$$

Solution Steps

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

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

Use the distributive property to multiply -2 by x^{2}-4x+4.

$$-2x^{2}+8x-8-3\left(x-2\right)+5$$

Use the distributive property to multiply -3 by x-2.

$$-2x^{2}+8x-8-3x+6+5$$

Combine 8x and -3x to get 5x.

$$-2x^{2}+5x-8+6+5$$

Add -8 and 6 to get -2.

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

Add -2 and 5 to get 3.

$$-2x^{2}+5x+3$$