Solve -(x^2-3x+2)^2-3(x^2-3x+2)+2

$$- ( x ^ { 2 } - 3 x + 2 ) ^ { 2 } - 3 ( x ^ { 2 } - 3 x + 2 ) + 2$$

Evaluate

$$-x^{4}+6x^{3}-16x^{2}+21x-8$$

Solution Steps

Square x^{2}-3x+2.

$$-\left(x^{4}-6x^{3}+13x^{2}-12x+4\right)-3\left(x^{2}-3x+2\right)+2$$

To find the opposite of x^{4}-6x^{3}+13x^{2}-12x+4, find the opposite of each term.

$$-x^{4}+6x^{3}-13x^{2}+12x-4-3\left(x^{2}-3x+2\right)+2$$

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

$$-x^{4}+6x^{3}-13x^{2}+12x-4-3x^{2}+9x-6+2$$

Combine -13x^{2} and -3x^{2} to get -16x^{2}.

$$-x^{4}+6x^{3}-16x^{2}+12x-4+9x-6+2$$

Combine 12x and 9x to get 21x.

$$-x^{4}+6x^{3}-16x^{2}+21x-4-6+2$$

Subtract 6 from -4 to get -10.

$$-x^{4}+6x^{3}-16x^{2}+21x-10+2$$

Add -10 and 2 to get -8.

$$-x^{4}+6x^{3}-16x^{2}+21x-8$$

Expand

$$-x^{4}+6x^{3}-16x^{2}+21x-8$$

Solution Steps

Square x^{2}-3x+2.

$$-\left(x^{4}-6x^{3}+13x^{2}-12x+4\right)-3\left(x^{2}-3x+2\right)+2$$

To find the opposite of x^{4}-6x^{3}+13x^{2}-12x+4, find the opposite of each term.

$$-x^{4}+6x^{3}-13x^{2}+12x-4-3\left(x^{2}-3x+2\right)+2$$

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

$$-x^{4}+6x^{3}-13x^{2}+12x-4-3x^{2}+9x-6+2$$

Combine -13x^{2} and -3x^{2} to get -16x^{2}.

$$-x^{4}+6x^{3}-16x^{2}+12x-4+9x-6+2$$

Combine 12x and 9x to get 21x.

$$-x^{4}+6x^{3}-16x^{2}+21x-4-6+2$$

Subtract 6 from -4 to get -10.

$$-x^{4}+6x^{3}-16x^{2}+21x-10+2$$

Add -10 and 2 to get -8.

$$-x^{4}+6x^{3}-16x^{2}+21x-8$$