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(-7w^2 - 2w - 1) - (-5w^2 + 3w - 2)
first get rid of the parentheses
(-7w^2 - 2w - 1) - (-5w^2 + 3w - 2)
= -7w^2 - 2w - 1 + 5w^2 - 3w + 2
now collect like powers
-7w^2+5w^2 - 2w-3w -1+2
-2w^2 - 5w + 1
Ah, the beautiful world of algebraic expressions! Let's tackle this together.
First, let's distribute the negative sign to each term in the second set of parentheses. We get:
-7w^2 - 2w - 1 + 5w^2 - 3w + 2
Now, let's combine like terms. We have -7w^2 + 5w^2, which simplifies to -2w^2. And we have -2w - 3w, which simplifies to -5w. Finally, we have -1 + 2, which simplifies to 1.
So, putting it all together, the expression (-7w^2 - 2w - 1) - (-5w^2 + 3w - 2) simplifies to:
-2w^2 - 5w + 1
Phew! We did it! If you have any more questions or need assistance with anything else, feel free to ask!
To simplify the given expression (-7w^2 - 2w - 1) - (-5w^2 + 3w - 2), you can follow these steps:
Step 1: Distribute the negative sign to the terms inside the parentheses on the right side:
-7w^2 - 2w - 1 + 5w^2 - 3w + 2
Step 2: Now, group like terms together. Combine the terms with the same exponent (w^2), the terms with the same exponent (w), and the constant terms:
(-7w^2 + 5w^2) + (-2w - 3w) + (-1 + 2)
Simplifying each group, we get:
-2w^2 - 5w + 1
So, the simplified form of the expression (-7w^2 - 2w - 1) - (-5w^2 + 3w - 2) is -2w^2 - 5w + 1.
To simplify the expression (-7w^2 - 2w - 1) - (-5w^2 + 3w - 2), we need to follow the order of operations, which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right).
Step 1: Distribute the negative sign to every term inside the parentheses of the second expression:
(-7w^2 - 2w - 1) + (5w^2 - 3w + 2)
Step 2: Combine like terms by adding or subtracting coefficients of like terms. In this case, we will gather the like terms together:
(-7w^2 + 5w^2) + (-2w - 3w) + (-1 + 2)
Step 3: Combine the like terms, starting with the highest exponent and moving towards the lowest:
(-7 + 5)w^2 + (-2 - 3)w + (-1 + 2)
Step 4: Simplify each term:
-2w^2 - 5w + 1
Therefore, the simplified form of the expression (-7w^2 - 2w - 1) - (-5w^2 + 3w - 2) is -2w^2 - 5w + 1.