Question

A rectangle has a height of 6k3 and a width of 2k2 + 4k +5.

Express the area of the entire rectangle.

Your answer should be a polynomial in standard form.

Answer 1

Answer:
`12k^5+24k^4+30k^3`

Explanation:

Given : The height of the rectangle =
`6k^3`

The width of the rectangle =
`2k^2+4k+5`

Formula : Area = height x width

Therefore , the area of triangle in terms of polynomial will be :

`6k^3*( 2k^2+4k+5)\\\\= 6k^3(2k^2)+6k^3(4k)+6k^3(5)\ \ [\text{Using Distributive property}]\\\\=12k^(3+2)+24k^(3+1)+30k^3\ \ [\text{Using exponents rule}:\ a^n* a^m=a^(n+m)]\\\\=12k^5+24k^4+30k^3`

Hence, the area of the entire rectangle =
`12k^5+24k^4+30k^3`