The area of room A is (5x^2-7x-6)ft^2. Room B has an area of (8x^2+6x-1)ft^2. If room A is the larger room, how much greater is the area of room A than the area of room B?
To find the difference in area between room A and room B, we need to subtract the area of room B from the area of room A:
(5x^2-7x-6)ft^2 - (8x^2+6x-1)ft^2
Simplifying, we can combine like terms:
= 5x^2 - 7x - 6 - 8x^2 - 6x + 1
= -3x^2 - 13x - 5
Therefore, the difference in area between room A and room B is (-3x^2 - 13x - 5)ft^2.
In the expression –7x-5x^2+5, what is the coefficient of x?
The coefficient of x is the number that appears directly in front of the x variable. In the expression –7x-5x^2+5, the coefficient of x is -7.
Write the expression using a single exponent. 2^2 x 2^8
When we multiply two numbers with the same base, we add the exponents. Using this rule, we can simplify 2^2 x 2^8 as:
2^(2+8) = 2^10
Therefore, 2^2 x 2^8 can be simplified as 2^10.
To find the difference in area between room A and room B, we need to subtract the area of room B from the area of room A.
The area of room A is (5x^2 - 7x - 6) ft^2.
The area of room B is (8x^2 + 6x - 1) ft^2.
To calculate the difference, we subtract the area of room B from the area of room A:
Area of room A - Area of room B = (5x^2 - 7x - 6) - (8x^2 + 6x - 1)
To subtract these two polynomials, we need to combine like terms.
First, let's distribute the negative sign to the terms inside the parentheses in the expression (8x^2 + 6x - 1):
Area of room A - Area of room B = 5x^2 - 7x - 6 - 8x^2 - 6x + 1
Now, let's rearrange the terms by gathering like terms together:
Area of room A - Area of room B = (5x^2 - 8x^2) + (-7x - 6x) + (-6 + 1)
Simplifying each set of like terms:
Area of room A - Area of room B = -3x^2 - 13x - 5
Therefore, the area of room A is (3x^2 + 13x + 5) ft^2 greater than the area of room B.