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Question
Factorize each of the following algebraic expression:
a2 + 14a + 48
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Solution
\[\text{ To factorise }a^2 + 14a + 48, \text{ we will find two numbers p and q such that }p + q = 14\text{ and }pq = 48 . \]
Now,
\[8 + 6 = 14 \]
and
\[8 \times 6 = 48\]
\[\text{ Splitting the middle term 14a in the given quadratic as }8a + 6a,\text{ we get: }\]
\[ a^2 + 14a + 48 = a^2 + 8a + 6a + 48\]
\[ = ( a^2 + 8a) + (6a + 48)\]
\[ = a(a + 8) + 6(a + 8)\]
\[ = (a + 6)(a + 8)\]
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