Question

find the area of the rectangle. simplify your answer. 5s² - 9s 3t² + t

Explanation:

Step1: Recall area formula for rectangle

The area \( A \) of a rectangle is given by the product of its length and width, i.e., \( A=\text{length} \times \text{width} \). Here, length is \( 5s^{2}-9s \) and width is \( 3t^{2}+t \). So, we need to multiply these two binomials: \( A=(5s^{2}-9s)(3t^{2}+t) \).

Step2: Apply distributive property (FOIL method)

Using the distributive property (also known as the FOIL method for binomials, though here we have two binomials with different variables, but the principle of distribution still holds), we multiply each term in the first binomial by each term in the second binomial:
\[

$$\begin{align*} (5s^{2}-9s)(3t^{2}+t)&=5s^{2}\times3t^{2}+5s^{2}\times t-9s\times3t^{2}-9s\times t\\ &=15s^{2}t^{2}+5s^{2}t - 27st^{2}-9st \end{align*}$$

\]

Answer:

\( 15s^{2}t^{2}+5s^{2}t - 27st^{2}-9st \)