Question

Write a polynomial that represents the area of the square. an area model. it has x and 4 along the length and x and 4 along the width. the partial products are shown as blank. a) x² + 8x + 16 b) x² - 8x + 16 c) x² - 8x - 16 d) x² + 8x - 16

Answer 1

The area of the square with a side length expression of (x+4) is found by squaring the expression, which results in the polynomial x² + 8x + 16.

Step-by-step explanation:

The area of a square is calculated by squaring the length of one side. In this case, the side of the square is represented by the expression (x+4). To find the area, we multiply this expression by itself:

(x + 4) × (x + 4)

Using the distributive property (also known as the FOIL method for binomials), we get:

x × x = x²
x × 4 = 4x
4 × x = 4x
4 × 4 = 16

Combining like terms, we add 4x and 4x to get 8x, and the final polynomial representing the area of the square is:

x² + 8x + 16

Therefore, the correct answer is:

(a) x² + 8x + 16