Question

1. \frac{(p + 1)(p - 10)}{6(p + 1)} \cdot \frac{6(p - 2)}{10 - p}

Explanation:

Write the expression as a single product

$$ \frac{(p+1)(p-10)}{6(p+1)} \cdot \frac{6(p-2)}{10-p} = \frac{6(p+1)(p-10)(p-2)}{6(p+1)(10-p)} $$

Cancel common factors

$$ \frac{6(p+1)(p-10)(p-2)}{6(p+1)(10-p)} = \frac{(p-10)(p-2)}{10-p} $$

Simplify opposite factors

$$ \frac{(p-10)(p-2)}{-(p-10)} = -(p-2) = 2-p $$

Answer:

\(2-p\)