simplify (9x^3+2x^2-5x+4)-(5x^3-7x+4) show your steps.
combine like terms
... the signs in the 2 polynomial are reversed by the preceding minus
(9x^3 - 5x^3) + 2x^2 + (-5x + 7x) + (4 + 4)
Lose the (4 + 4)
To simplify the expression (9x^3 + 2x^2 - 5x + 4) - (5x^3 - 7x + 4), you need to perform the subtraction operation between the terms within the parentheses. Here are the steps:
Step 1: Distribute the subtraction sign (-) to each term inside the second set of parentheses to change the signs of those terms:
(9x^3 + 2x^2 - 5x + 4) - 5x^3 + 7x - 4
Step 2: Combine like terms by grouping the terms with similar powers of x together:
(9x^3 - 5x^3) + 2x^2 + (-5x + 7x) + (4 - 4)
Step 3: Perform the subtraction of the coefficients separately:
4x^3 + 2x^2 + 2x + 0
Step 4: Remove any term with a coefficient of 0:
4x^3 + 2x^2 + 2x
Therefore, the simplified form of (9x^3 + 2x^2 - 5x + 4) - (5x^3 - 7x + 4) is 4x^3 + 2x^2 + 2x.