Hello! My question is if I had a polynomial like this:
(5x^2-3x) -(7x-12+3^2)
Would that 7x be negative? Because I have a problem similar to this and I wasn't sure whether to subtract "7x" or add it.
Thank you!
yes.
after removing the parentheses, that would be the same as adding
-7x+12-3x^2
yes ... the minus sign outside the parentheses changes all the signs inside the parentheses
Thank you!
Hello! When subtracting a term like "7x" in your polynomial expression, it would indeed be considered as a negative term. Let me explain how you can determine whether the term should be subtracted or added.
In your polynomial expression, we have:
(5x^2 - 3x) - (7x - 12 + 3^2)
To simplify this expression, we can distribute the negative sign inside the parentheses:
(5x^2 - 3x) - 7x + 12 - 3^2
Now, let's focus on the "-7x" term. The rule for subtracting a term is that when a negative sign is in front of the parentheses, like "- (7x - 12 + 3^2)", you distribute the negative sign to every term inside the parentheses.
So, "- (7x - 12 + 3^2)" becomes "-7x + 12 - 3^2". This means that "7x" turns into "-7x".
Therefore, the expression simplifies to:
(5x^2 - 3x) - 7x + 12 - 9
Now, you can combine like terms, starting with the x-terms:
5x^2 - 3x - 7x + 12 - 9
Finally, combine the x-terms and the constant terms:
5x^2 - 10x + 3
Overall, the "-7x" term from your original polynomial expression becomes a negative term when simplified. Remember to distribute the negative sign when subtracting a term inside parentheses.
I hope this explanation helps! Let me know if you have any further questions.