# Factorize Each of the Following Algebraic Expression: (A + 7)(A − 10) + 16 - Mathematics

Sum

Factorize each of the following algebraic expression:
(a + 7)(a − 10) + 16

#### Solution

$(a + 7)(a - 10) + 16$
$= a^2 - 10a + 7a - 70 + 16$
$= a^2 - 3a - 54$
$\text{ To factorise }a^2 - 3a - 54 ,\text{ we will find two numbers p and q such that }p + q = - 3\text{ and }pq = - 54 .$
Now,
$6 + ( - 9) = - 3$
and
$6 \times ( - 9) = - 54$
$\text{ Splitting the middle term }- 3a \text{ in the given quadratic as } - 9a + 6a, \text{ we get: }$
$a^2 - 3a - 54 = a^2 - 9a + 6a - 54$
$= ( a^2 - 9a) + (6a - 54)$
$= a(a - 9) + 6(a - 9)$
$= (a + 6)(a - 9)$

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 7 Factorization
Exercise 7.7 | Q 13 | Page 27