Q9 Simplify and write your final answer in factored form.
(9r ^ 3 + 2r ^ 2 - 5r + 4) - (5r ^ 3 - 7r + 4)
First, combine like terms within each set of parentheses:
(9r^3 + 2r^2 - 5r + 4) - (5r^3 - 7r + 4)
= 9r^3 + 2r^2 - 5r + 4 - 5r^3 + 7r - 4
Next, combine like terms by adding or subtracting coefficients:
= (9r^3 - 5r^3) + 2r^2 + (-5r + 7r) + 4 + (-4)
= 4r^3 + 2r^2 + 2r
Therefore, the final answer in factored form is:
4r^3 + 2r^2 + 2r