Question
Solve: $q^2-10 p+21$
✓
Answer
$q^2-10 p+21$
$\left.=q^2-10 q+\left(\frac{10}{2}\right)^2-\left(\frac{10}{2}\right)^2+21 \text { [Adding and subtracting }\left(\frac{10}{2}\right)^2, \text { that is } 5^2\right] $
$=q 2-2 \times q \times 5+5^2-5^2+21$
$=(q-5) 2-4[\text { completing the square }]$
$=[(q-5)-2][(q-5)+2]$
$=(q-5-2)(q-5+2)$
$=(q-7)(q-3)$
$\left.=q^2-10 q+\left(\frac{10}{2}\right)^2-\left(\frac{10}{2}\right)^2+21 \text { [Adding and subtracting }\left(\frac{10}{2}\right)^2, \text { that is } 5^2\right] $
$=q 2-2 \times q \times 5+5^2-5^2+21$
$=(q-5) 2-4[\text { completing the square }]$
$=[(q-5)-2][(q-5)+2]$
$=(q-5-2)(q-5+2)$
$=(q-7)(q-3)$
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