Question

BINGO A bingo card contains 25 square spaces arranged into a larger square. 24 of the squares are labeled with numbers and the center square is labeled as a free space. The expression 16 - x² represents total area of the squares labeled with numbers. Factor the expression. ​

Answer 1

(4 + x)(4 - x).

Explanation:

The expression 16 - x² can be factored as the difference of two squares:

(4 + x)(4 - x)

To see why this is true, notice that:

(4 + x)(4 - x) = 16 - x²

This is a special case of the identity:

(a + b)(a - b) = a² - b²

where a = 4 and b = x. Using this identity, we get:

(4 + x)(4 - x) = 4² - x² = 16 - x²

Therefore, the expression 16 - x² can be factored as (4 + x)(4 - x).