Question
Factorise the expressions: $q^2- 10q + 21$
✓
Answer
$q^2– 10q + 21$
$= q^2– 10q + 25 – 4$
$= {(q)^2– 2(q) (5) + (5)^2} – 4$
$= (q – 5)^2– (2)^2. . . .$ [Using Identity $II]$
$= (q – 5 – 2) (q – 5 + 2). . . .$ [Using Identity $III]$
$= (q – 7) (q – 3)$
$= q^2– 10q + 25 – 4$
$= {(q)^2– 2(q) (5) + (5)^2} – 4$
$= (q – 5)^2– (2)^2. . . .$ [Using Identity $II]$
$= (q – 5 – 2) (q – 5 + 2). . . .$ [Using Identity $III]$
$= (q – 7) (q – 3)$
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