write a polynomial that represents the area of the square.
13.
7n - 5

find the product.
22. (7m + 8n)(7m - 8n)

Question

write a polynomial that represents the area of the square.
13.
    7n - 5

find the product.
22. (7m + 8n)(7m - 8n)

Accepted Answer

### Problem 13: Write a polynomial that represents the area of the square.
# Explanation:
## Step1: Recall the area formula for a square.
The area $ A $ of a square with side length $ s $ is given by $ A = s^2 $. Here, the side length of the square is $ 7n - 5 $, so we need to square this binomial.

## Step2: Apply the formula $(a - b)^2 = a^2 - 2ab + b^2$.
Let $ a = 7n $ and $ b = 5 $. Then:
$$
\begin{align*}
(7n - 5)^2 &= (7n)^2 - 2(7n)(5) + 5^2 \
&= 49n^2 - 70n + 25
\end{align*}
$$

# Answer:
The polynomial representing the area of the square is $ 49n^2 - 70n + 25 $.

### Problem 22: Find the product $(7m + 8n)(7m - 8n)$.
# Explanation:
## Step1: Recognize the difference of squares formula.
The formula for the product of a sum and a difference is $ (a + b)(a - b) = a^2 - b^2 $. Here, $ a = 7m $ and $ b = 8n $.

## Step2: Apply the difference of squares formula.
Substitute $ a = 7m $ and $ b = 8n $ into the formula:
$$
\begin{align*}
(7m + 8n)(7m - 8n) &= (7m)^2 - (8n)^2 \
&= 49m^2 - 64n^2
\end{align*}
$$

# Answer:
The product is $ 49m^2 - 64n^2 $.

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QUESTION IMAGE

Question

Explanation:

Problem 13: Write a polynomial that represents the area of the square.

Step1: Recall the area formula for a square.

Step2: Apply the formula \((a - b)^2 = a^2 - 2ab + b^2\).

Step1: Recognize the difference of squares formula.

Step2: Apply the difference of squares formula.

Answer:

Problem 22: Find the product \((7m + 8n)(7m - 8n)\).