Question

A rectangle has a height of a^2+3 and a width of a^2 +2a+5

Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.

Answer 1

Area = a^4 + 10 a^2 + 6 a + 15

Explanation:

Height: a^2+3

Width: a^2 +2a+5

Area of the entire rectangle = Height x Width

So we have to multiply both expressions and apply distributive property:

Area = (a^2 + 3) x (a^2 + 2a + 5)

Area = a^2 x (a^2 + 2a + 5) + 3 x (a^2 +2a + 5)

Area = a^4 + 2a^2 + 5a^2 + 3a^2 + 6a + 15

grouping terms of same power of a:

Area = a^4 + (2+5+3)a^2 + 6a + 15

Area = a^4 + 10 a^2 + 6 a + 15