–7w2 – 2w – 1) – (–5w2 + 3w – 2)
A. 12w2 + 5w + 1
B. –2w2 – 5w – 1
C. –2w2 – 5w + 1
D. –12w2 – 5w – 3
First, we need to distribute the negative sign in front of the second set of parentheses:
-7w2 - 2w - 1 + 5w2 - 3w + 2
Next, we can combine like terms:
-2w2 - 5w + 1
Therefore, the answer is C. -2w2 - 5w + 1.
Look at the given rectangle. Write a polynomial expression in simplest form for the perimeter of the rectangle.
rectangle
A. 10x + 10 + 4x – 2
B. 14x + 12
C. 14x + 8
D. 2(5x + 5) + 2(2x – 1)
The perimeter of a rectangle is found by adding up the lengths of all four sides. In this case, the top and bottom sides are each of length 5x+5, and the left and right sides are each of length 2x-1. Therefore, the perimeter is:
2(5x+5) + 2(2x-1)
Simplifying this expression, we get:
10x + 10 + 4x - 2
Combining like terms, we get:
14x + 8
Therefore, the answer is C. 14x + 8.
To simplify the expression –7w^2 – 2w – 1) – (–5w^2 + 3w – 2), we should distribute the negative sign to every term inside the parentheses:
–7w^2 – 2w – 1 + 5w^2 – 3w + 2
Next, we can combine like terms:
(-7w^2 + 5w^2) + (-2w - 3w) + (-1 + 2)
Simplifying further:
-2w^2 - 5w + 1
Therefore, the simplified expression is –2w^2 – 5w + 1.
So, the correct answer is option C: –2w^2 – 5w + 1.