Question

Factorize each of the following algebraic expression:
25 − p² − q² − 2pq

Answer 1

\[25 - p^2 - q^2 - 2pq\]
\[ = 25 - ( p^2 + 2pq + q^2 )\]
\[ = 5^2 - ( p^2 + 2 \times p \times q + q^2 )\]
\[ = 5^2 - (p + q )^2 \]
\[ = [5 - (p + q)][5 + (p + q)]\]
\[ = (5 - p - q)(5 + p + q)\]
\[ = - (p + q - 5)(p + q + 5)\]