Answer: [tex]12k^5+24k^4+30k^3[/tex]
Step-by-step explanation:
Given : The height of the rectangle = [tex]6k^3[/tex]
The width of the rectangle = [tex]2k^2+4k+5[/tex]
Formula : Area = height x width
Therefore , the area of triangle in terms of polynomial will be :
[tex]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[/tex]
Hence, the area of the entire rectangle =[tex]12k^5+24k^4+30k^3[/tex]
