Maharashtra BoardEnglish MediumSTD 8MathsFactorization4 Marks
Question
Factories:
$(a+7)(a-10)+16$
✓
Answer
$(a+7)(a-10)+16$
$=a^2-10 a+7 a-70+16$
$=a^2-3 a-54$
To factories $a^2-3 a-54$, we will find two numbers $p$ and $q$ such that $p+q=-3$ and $p q=-54$
Now，
$6+(-9)=-3 \text { And } 6 \times(-9)=-54$
Splitting the middle term $-3 a$ in the given quadratic as $-9+6 a$, we get:
$a^2-3 a-54=a^2-9 a+6 a-54$
$=\left(a^2-9 a\right)+(6 a-5)$
$=a(a-9)+6(a-9)$
$=(a+6)(a-9)$
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