Question:
Give the possible expression for the length \& breadth of the rectangle having $35 y^{2}-13 y-12$ as its area.
Solution:
Area is given as $35 y^{2}-13 y-12$
Splitting the middle term,
Area $=35 y^{2}+218 y-15 y-12$
$=7 y(5 y+4)-3(5 y+4)$
$=(5 y+4)(7 y-3)$
We also know that area of rectangle = length × breadth
∴ Possible length = (5y + 4) and breadth = (7y − 3)
Or possible length = (7y − 3) and breadth = (5y + 4)
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