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Factorization — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSFactorization5 Marks
Question
Solve:
$4y^2+ 12y + 5$
✓

Answer

$4y^2+ 12y + 5$
$4\Big(\text{y}^2=3\text{y}+\frac{5}{4}\Big)$ [ making the co-efficient of $y^2$]
$4\Big[\text{y}^2+3\text{y}+\Big(\frac{3}{2}\Big)^2-\Big(\frac{3}{2}\Big)^2=\frac{5}{4}$ $\Bigg[$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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