Question

I’m trying to help my sister. I don’t know what to do.

Answer 1

Area of the rectangle $=2t^3+15t^2+19t+6$.

Solution:

Given data:

Height of a rectangle = $t^2+7t+6$

Width of a rectangle = $2t+1$

Area of the rectangle = height × width

                                   $=(t^2+7t+6)\times(2t+1)$

Multiply each term of height with the each term of width.

                                  $=(t^2+7t+6)2t+(t^2+7t+6)1$

                                  $=(2t^3+14t^2+12t)+(t^2+7t+6)$

                                  $=2t^3+14t^2+12t+t^2+7t+6$

Adding like terms of the polynomial.

                                  $=2t^3+15t^2+19t+6$

Therefore, Area of the rectangle $=2t^3+15t^2+19t+6$.