Question

the rectangular area of the new school courtyard is represented by the expression: $25m^2 - 16$. which expression represents the length and width of the courtyard?
a $(5m - 4)(5m + 4)$
b $(25m - 4)(m + 4)$
c cannot determine
d $(5m - 4)^2$

Explanation:

Step1: Recall the difference of squares formula

The difference of squares formula is \(a^2 - b^2=(a - b)(a + b)\).

Step2: Identify \(a\) and \(b\) in the given expression

In the expression \(25m^2-16\), we can rewrite \(25m^2\) as \((5m)^2\) and \(16\) as \(4^2\). So, \(a = 5m\) and \(b = 4\).

Step3: Apply the difference of squares formula

Using the formula \(a^2 - b^2=(a - b)(a + b)\), we substitute \(a = 5m\) and \(b = 4\) to get \((5m - 4)(5m + 4)\).

Step4: Check other options (optional but helpful)

• Option B: Expand \((25m - 4)(m + 4)=25m^2+100m-4m - 16=25m^2 + 96m-16

eq25m^2-16\).

• Option D: Expand \((5m - 4)^2=(5m)^2-2\times5m\times4 + 4^2=25m^2-40m + 16

eq25m^2-16\).

• Option C is incorrect as we can determine the factors.

Answer:

A. \((5m - 4)(5m + 4)\)