Question
Factorize of the following expressions:
$p^2q − pr^2− pq + r^2$
$p^2q − pr^2− pq + r^2$
✓
Answer
$p^2q − pr^2− pq + r^2$
$= (p^2q - pq) + (r^2- pr^2) $
$pq(p -1) + r^2(1 - p) $
$pq(p -1) - r^2(P -1) [$SINCE, $(1 - P) = -(P -1)] $
$= (pq - r^2)(p - 1) [$taking $(p - 1)$ as the common factor$]$
$= (p^2q - pq) + (r^2- pr^2) $
$pq(p -1) + r^2(1 - p) $
$pq(p -1) - r^2(P -1) [$SINCE, $(1 - P) = -(P -1)] $
$= (pq - r^2)(p - 1) [$taking $(p - 1)$ as the common factor$]$
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