Note: Enter your answer and show all the steps that you use to solve this problem and write your final answer in factored form in the space provided.
Simplify:
(9x^3+2x^2−5x+4)−(5x^3−7x+4)
To simplify this expression, we need to distribute the negative sign to every term inside the second set of parentheses:
(9x^3 + 2x^2 - 5x + 4) - (5x^3 - 7x + 4)
= 9x^3 + 2x^2 - 5x + 4 - 5x^3 + 7x - 4
Next, we need to combine like terms:
(9x^3 - 5x^3) + (2x^2) + (-5x + 7x) + (4 - 4)
= 4x^3 + 2x^2 + 2x
Finally, we can factor out a common term of 2x:
2x(2x^2 + x + 1)
Therefore, the simplified expression in factored form is 2x(2x^2 + x + 1).
To simplify the expression (9x^3+2x^2−5x+4)−(5x^3−7x+4), let's combine like terms by subtracting the quantities inside the parentheses.
Step 1: Distribute the negative sign to all terms inside the second parentheses:
(9x^3+2x^2−5x+4)−5x^3+7x−4
Step 2: Combine like terms:
9x^3 - 5x^3 + 2x^2 - 5x + 7x + 4 - 4
Step 3: Simplify the polynomial:
(9x^3 - 5x^3) + 2x^2 + (-5x + 7x) + (4 - 4)
4x^3 + 2x^2 + 2x
The simplified expression is:
4x^3 + 2x^2 + 2x in factored form.
To simplify the given expression, (9x^3+2x^2−5x+4)−(5x^3−7x+4), we need to combine like terms.
First, let us expand the parentheses in the expression:
(9x^3 + 2x^2 − 5x + 4) − (5x^3 − 7x + 4)
= 9x^3 + 2x^2 − 5x + 4 − 5x^3 + 7x − 4
Next, let's combine the like terms:
= (9x^3 - 5x^3) + 2x^2 + (-5x + 7x) + (4 - 4)
= 4x^3 + 2x^2 + 2x
Therefore, the simplified expression is:
4x^3 + 2x^2 + 2x