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: $12k^5+24k^4+30k^3$

Step-by-step 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 :

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

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