Question
Solve:(y - 3)(y - 4)
✓
Answer
(y - 3)(y - 4)= y2 - 7y + 12 $\Big[$Adding and subtracting $\Big(\frac{7}{2}\Big)^2\Big]$
$=\text{y}^2-7\text{y}+\Big(\frac{7}{2}\Big)^2-\Big(\frac{7}{2}\Big)^2+12$
Comleting the square
$=\Big(\text{y}-\Big(\frac{7}{2}\Big)\Big)^2-\frac{49}{4}+\frac{48}{4}$
$=\Big(\text{y}-\Big(\frac{7}{2}\Big)\Big)^2-\Big(\frac{1}{4}\Big)$
$=\Big(\text{y}-\Big(\frac{7}{2}\Big)^2-\Big(\frac{1}{2}^2\Big)$
$=\Big[\text{y}-\Big(\frac{7}{2}-\frac{1}{2}\Big)\Big]\Big[\text{y}-\Big(\frac{7}{2}+\frac{1}{2}\Big)\Big]$
$=(\text{y}-4)(\text{y}-3)$
$=\text{y}^2-7\text{y}+\Big(\frac{7}{2}\Big)^2-\Big(\frac{7}{2}\Big)^2+12$
Comleting the square
$=\Big(\text{y}-\Big(\frac{7}{2}\Big)\Big)^2-\frac{49}{4}+\frac{48}{4}$
$=\Big(\text{y}-\Big(\frac{7}{2}\Big)\Big)^2-\Big(\frac{1}{4}\Big)$
$=\Big(\text{y}-\Big(\frac{7}{2}\Big)^2-\Big(\frac{1}{2}^2\Big)$
$=\Big[\text{y}-\Big(\frac{7}{2}-\frac{1}{2}\Big)\Big]\Big[\text{y}-\Big(\frac{7}{2}+\frac{1}{2}\Big)\Big]$
$=(\text{y}-4)(\text{y}-3)$
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