Question
Factories:
$(a + 7)(a - 10) + 16$
$(a + 7)(a - 10) + 16$
✓
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 $pq = -54$
Now,
$6 + (-9) = -3$ And $6 x (-9) = -54$
Splitting the middle term $-3a$ in the given quadratic as $-9 + 6a$,
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)$
$ =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 $pq = -54$
Now,
$6 + (-9) = -3$ And $6 x (-9) = -54$
Splitting the middle term $-3a$ in the given quadratic as $-9 + 6a$,
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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