Question

A rectangle has a height of b3 + b2 and a width of b2 + 7b + 4. Express the area of the entire rectangle.

A. b ⁵ +14b ³ +52b² +56b+16
B. b⁵+14b ⁴+49b³ +7b² +28b+16
C. Both a and b
D. None of the above

Answer 1

The area of the rectangle is b5 + 8b4 + 11b3 + 4b2.

Step-by-step explanation:

The area of a rectangle is found by multiplying its height by its width. In this case, the height of the rectangle is b3 + b2 and the width is b2 + 7b + 4. To find the area, we multiply the two expressions:

Area = (b3 + b2) * (b2 + 7b + 4)

To simplify, we can use the distributive property and multiply each term in the first expression by each term in the second expression:

Area = b3 * b2 + b3 * 7b + b3 * 4 + b2 * b2 + b2 * 7b + b2 * 4

Finally, we combine like terms to simplify:

Area = b5 + 7b4 + 4b3 + b4 + 7b3 + 4b2

Combining like terms gives us the final expression:

Area = b5 + 8b4 + 11b3 + 4b2