solve step-by-step
(9x^3 + 2x^2 - 5x + 4) - (5x^3 - 7x + 4)
First, simplify the expression by combining like terms inside the parentheses:
(9x^3 + 2x^2 - 5x + 4) - (5x^3 - 7x + 4)
= 9x^3 + 2x^2 - 5x + 4 - 5x^3 + 7x - 4
= (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.
explain step two
In step two, we are expanding the expression by removing the parentheses and combining like terms.
The original expression is: (9x^3 + 2x^2 - 5x + 4) - (5x^3 - 7x + 4)
We can distribute the negative sign to all terms inside the second set of parentheses:
= 9x^3 + 2x^2 - 5x + 4 - 5x^3 + 7x - 4
Next, we combine the like terms. Like terms are terms that have the same variable raised to the same power.
- Combine the x^3 terms: 9x^3 - 5x^3 = 4x^3
- Combine the x^2 terms: 2x^2
- Combine the x terms: -5x + 7x = 2x
- Combine the constant terms: 4 - 4 = 0
Therefore, the resulting expression after combining like terms is: 4x^3 + 2x^2 + 2x
I don't understand why the signs need to switch
I see the confusion. Let's break it down with a more detailed explanation:
Original expression: (9x^3 + 2x^2 - 5x + 4) - (5x^3 - 7x + 4)
When you distribute the negative sign inside the second set of parenthesis, it changes the sign of each term inside the parentheses. So, it's like multiplying each term inside the second set of parentheses by -1.
Here's the step with emphasis on the changes in signs:
= 9x^3 + 2x^2 - 5x + 4 - 5x^3 + 7x - 4
= 9x^3 + 2x^2 - 5x + 4 + (-5x^3) + (-7x) + (-4)
After distributing the negative sign to each term inside the second set of parentheses, it effectively changes the sign of those terms when they are brought out of the parentheses.
I hope this clears up the confusion. Please let me know if you need further clarification.