Question
Divide: $z(5z^2- 80)$ by $5z(z + 4)$
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Answer
$z(5z^2– 80)$
$= z[(5 \times z^2) – (5 \times 16)]$
$= z \times 5 \times (z^2– 16)$
$= 5z(z + 4)(z – 4)$ [using the identity $a^2– b^2= (a + b) (a – b)]$
Thus, $z(5z^2– 80) ÷ 5z(z + 4)$
$= \frac{5 z(z-4)(z+4)}{5 z(z+4)} = (z – 4)$
$= z[(5 \times z^2) – (5 \times 16)]$
$= z \times 5 \times (z^2– 16)$
$= 5z(z + 4)(z – 4)$ [using the identity $a^2– b^2= (a + b) (a – b)]$
Thus, $z(5z^2– 80) ÷ 5z(z + 4)$
$= \frac{5 z(z-4)(z+4)}{5 z(z+4)} = (z – 4)$
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