Simplify completely and arrange in descending order: (-2-x)(x^(2)-4x+1)-(x+3)(-x^(2)-2x+3)

Question

Not sure how to simplify this.

Answer 1

(-2-x)(x^(2)-4x+1)-(x+3)(-x^(2)-2x+3)

 

=(-2-x)(x² -4x +1 ) -(x+3)(-x² -2x +3)

 

use distributive property for both terms

 

= (-2x² +8x -2 -x³ + 4x² -x) - (-x³ -2x² +3x -3x² -6x +9)

 

combine like terms in parenthesis

 

=(-x³ +2x² +7x -2) -(-x³-5x² -3x +9)

 

remove the parenthesis

 

=-x³ +2x²+7x-2 +x³+5x²+3x-9

 

combine the like terms

 

=7x² + 10x -11

Answer 2

It's a lot easier to read & work with if you can use exponents and get rid of unnecessary parentheses.

 

(x²-4x+1) - (x+3)(-x²-2x+3) = (x² - 4x  +1) + (x+3)(x² + 2x -3).   Note that I applied the subtraction to the trinomial as a negative factor. This makes the next step easier.

 

Now YOU do this: multiply out the product of the parenthesized binomial and the parenthesized trinomial.

 

Finally, COMBINE LIKE terms.