UNIT 5
Polynomials and Properties of Exponents
LESSON 2
Adding and Subtracting Polynomials
The expression (9m + 6 + (-5m - 6)) can be simplified by first combining the like terms.
9m and -5m are like terms because they have the same variable m. When we add these terms, we get 9m + (-5m) = 4m.
6 and -6 are additive inverses of each other, so when we add them, we get 6 + (-6) = 0.
Therefore, the expression (9m + 6 + (-5m - 6)) simplifies to:
4m + 0
which is just:
4m
If none of the answer options match the simplified expression you got, it is possible that there was a mistake in the given options or the question was written incorrectly. In this case, you can check with your teacher or instructor to clarify the question or correct the options.
The given expression is:
(6h + 1) - (9h + 4)
To simplify this expression, we need to distribute the negative sign to the terms inside the parentheses and then combine the like terms, as follows:
6h + 1 - 9h - 4
Combine the like terms:
-3h - 3
Therefore, the simplified expression is:
-3h - 3
Whats the answer to (-7w^2-2w-1)-(-5w^2+3w-2)
Polynomials are mathematical expressions that consist of variables and coefficients, combined using addition, subtraction, multiplication, and division. Adding and subtracting polynomials is a basic operation in algebra that involves combining like terms to simplify the expression.
To add or subtract polynomials, we need to look for like terms. Like terms are terms that have the same variables and exponents. For example, 2x and 5x are like terms, while 2x and 5y are not. To add or subtract polynomials, we combine the coefficients of the like terms.
Let's look at an example:
3x^2 + 4x - 2 + 2x^2 - 3x + 1
To add these polynomials, we first group the like terms:
(3x^2 + 2x^2) + (4x - 3x) + (-2 + 1)
We then combine the coefficients of the like terms:
5x^2 + 1x - 1
So the answer is 5x^2 + x - 1.
When subtracting polynomials, we follow the same process, but we also need to distribute the negative sign to each term in the second polynomial before combining the like terms.
Let's look at another example:
4x^3 - 6x^2 + 3x - 2 - (2x^3 + 5x^2 - 2x + 1)
To subtract these polynomials, we first distribute the negative sign:
4x^3 - 6x^2 + 3x - 2 - 2x^3 - 5x^2 + 2x - 1
We then group the like terms:
(4x^3 - 2x^3) + (-6x^2 - 5x^2) + (3x + 2x) + (-2 - 1)
And finally, we combine the coefficients of the like terms:
2x^3 - 11x^2 + 5x - 3
So the answer is 2x^3 - 11x^2 + 5x - 3.
In summary, adding and subtracting polynomials involves combining like terms by adding or subtracting their coefficients. We need to be careful to distribute the negative sign when subtracting polynomials.
Whats the answers to (9m+6+(-5m-6)
Thanks now, whats the answer to (3r^+7r+1)+(4r^-8r-2)
The given expression is:
(3r^2 + 7r + 1) + (4r - 8r^2 - 2)
We can start by grouping the like terms together:
= (-8r^2 + 3r^2) + (4r + 7r) + (1 - 2)
= (-5r^2) + (11r) - 1
Therefore, the simplified expression is:
-5r^2 + 11r - 1
The choices for (3r^2 + 7r + 1) + (4r - 8r^2 - 2) that i have are
7r^2+15r-1
7r^2-r-1
7r^2-15r-3
-r^2-r-1
The correct answer is:
(3r^2 + 7r + 1) + (4r - 8r^2 - 2) = -5r^2 + 11r - 1
None of the given answer options match this simplification.
hu thats wird so what do i do?
ok thanks anyways
You're welcome! If you have any more questions, feel free to ask.
Whats the answer for (6h+1)-(9h+4)
thank you!
You're welcome! If you have any other questions, feel free to ask.
The given expression is:
(-7w^2 - 2w - 1) - (-5w^2 + 3w - 2)
When we subtract a negative, it is the same as adding the opposite, so:
(-7w^2 - 2w - 1) + (5w^2 - 3w + 2)
Group the like terms together:
=(-7w^2 + 5w^2) + (-2w - 3w) + (-1 + 2)
Simplify:
=-2w^2 - 5w + 1
Therefore, the simplified expression is:
-2w^2 - 5w + 1
thank you!
You're welcome! If you have any more questions, feel free to ask.
Ok so this is the last one but im not sure how to tell you what it is because its wierd
Sure, you can try to explain the problem to me and I will do my best to help you.
Ok it says "Look at the given rectangle. Write a polynomial expression in simplest form for the perimeter of the rectangle. and these are the numbers,
5x+5
2x-1
5x+5
2x-1
To find the perimeter of the rectangle, we need to add up the lengths of all four sides. The top and bottom sides are both 5x+5, and the left and right sides are both 2x-1. So, the perimeter P is:
P = (5x + 5) + (2x - 1) + (5x + 5) + (2x - 1)
Simplify:
P = 12x + 8
Therefore, the polynomial expression in simplest form for the perimeter of the rectangle is:
P = 12x + 8
Do you mean 14x+8 because there is not a 12x+8...
Sorry about that! You're absolutely right. I made a mistake in my calculation. The correct answer is:
P = (5x + 5) + (2x - 1) + (5x + 5) + (2x - 1)
P = 14x + 8
Therefore, the polynomial expression in simplest form for the perimeter of the rectangle is:
P = 14x + 8
OK OK OK THANK YOU SOOOOOO MUCH!!!!!!!!!!!!!!!!
You're welcome! I'm glad I could help. If you have any more questions in the future, feel free to ask!
(3r^2 + 7r + 1) + (4r^2 - 8r - 2)
We can start by grouping the like terms:
= (3r^2 + 4r^2) + (7r - 8r) + (1 - 2)
= (7r^2) - r - 1
Therefore, the simplified expression is:
7r^2 - r - 1