Maharashtra BoardEnglish MediumSTD 8MathsFactorization4 Marks
Question
Solve:
$4 y^2+12 y+5$
✓
Answer
$4 y^2+12 y+54\left(y^2=3 y+\frac{5}{4}\right)\left[\right.$ making the co-efficient of $\left.y^2\right]$
$4\Big[\text{y}^2+3\text{y}+\Big(\frac{3}{2}\Big)^2-\Big(\frac{3}{2}\Big)^2=\frac{5}{4}$ $\Bigg[$Adding and subtracting $\Big(\frac{3}{2}\Big)^2\Bigg]$
$=4\Big[(\text{y}+\frac{3}{2})^2-\frac{9}{4}+\frac{5}{4}\Big]$
$=4\Big[\Big(\text{y}+\frac{3}{2}\Big)^2-1\Big]$ [ completing the square]
$=4\Big[\Big(\text{y}+\frac{3}{2}-1\Big)\Big]\Big[\Big(\text{y}+\frac{3}{2}+1\Big)\Big]$
$=4\Big(\text{y}+\frac{3}{2}-1\Big)\Big(\text{y}+\frac{3}{2}-1\Big)$
$=4\Big(\text{y}+\frac{3}{2}\Big)\Big(\text{y}+\frac{3}{2}\Big)$
$=(2\text{y}+1)(2\text{y}+5)$
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