Factorise: $7 y^{2} + 49 y + 84$

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Solution

The given expression $7 y^{2} + 49 y + 84$ can be factorised as follows:

$7 y^{2} + 49 y + 84 = 7 (y^{2} + 7 y + 12) = 7 (y^{2} + 4 y + 3 y + 12) = 7 [y (y + 4) + 3 (y + 4)] = 7 (y + 3) (y + 4)$

Hence, $7 y^{2} + 49 y + 84 = 7 (y + 3) (y + 4)$

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