Question

1. \\(\frac{28p^3 - 28p^2}{8p^2} \cdot \frac{2}{28p^3 - 28p^2}\\)

Explanation:

Step1: Identify Common Factors

Notice that \(28p^3 - 28p^2\) appears in both the numerator of the first fraction and the denominator of the second fraction. Let's denote \(A = 28p^3 - 28p^2\) for simplicity. Then the expression becomes \(\frac{A}{8p^2} \cdot \frac{2}{A}\).

Step2: Cancel Common Terms

The \(A\) terms (i.e., \(28p^3 - 28p^2\)) in the numerator and denominator cancel out (assuming \(28p^3 - 28p^2
eq0\), which means \(p
eq0\) and \(p
eq1\)). So we are left with \(\frac{2}{8p^2}\).

Step3: Simplify the Fraction

Simplify \(\frac{2}{8p^2}\) by dividing the numerator and denominator by their greatest common divisor, which is 2. So \(\frac{2\div2}{8p^2\div2}=\frac{1}{4p^2}\).

Answer:

\(\frac{1}{4p^2}\)