Final answer:
The area of a rectangle with sides (4x+1) cm and (2x-5) cm is calculated by multiplication, applying the FOIL method, with the final formula being (8x² - 18x - 5) cm².
Step-by-step explanation:
To find the area of a rectangle, we need to multiply the length by the width. In this case, the length of the rectangle is (4x+1)cm and the width is (2x-5)cm.
When we multiply these two polynomials, we apply the distributive property of multiplication over addition, also known as FOIL method (First, Outer, Inner, Last):
- First, multiply the first terms in each binomial: (4x * 2x) = 8x²
- Outer, multiply the outer terms in the product: (4x * -5) = -20x
- Inner, multiply the inner terms: (1 * 2x) = 2x
- Last, multiply the last terms: (1 * -5) = -5
Combine like terms (-20x and 2x) to get -18x. So, the area of the rectangle is A = (8x² - 18x - 5) cm², which is not in the provided options.
Learn more about Area of a Rectangle