Area of the rectangle [tex]=2t^3+15t^2+19t+6[/tex].
Solution:
Given data:
Height of a rectangle = [tex]t^2+7t+6[/tex]
Width of a rectangle = [tex]2t+1[/tex]
Area of the rectangle = height × width
[tex]=(t^2+7t+6)\times(2t+1)[/tex]
Multiply each term of height with the each term of width.
[tex]=(t^2+7t+6)2t+(t^2+7t+6)1[/tex]
[tex]=(2t^3+14t^2+12t)+(t^2+7t+6)[/tex]
[tex]=2t^3+14t^2+12t+t^2+7t+6[/tex]
Adding like terms of the polynomial.
[tex]=2t^3+15t^2+19t+6[/tex]
Therefore, Area of the rectangle [tex]=2t^3+15t^2+19t+6[/tex].
