Question
Factorise the expression and divide them as directed: $4yz (z^2+ 6z – 16) \div 2y (z + 8)$
✓
Answer
$4yz (z^2+ 6z – 16) \div 2y (z + 8)$
$ = \frac{{4yz({z^2} + 6z - 16)}}{{2y(z + 8)}}$
$ = \frac{{2z({z^2} + 6z - 16)}}{{z + 8}}$
$ = \frac{{2z({z^2} + 8z - 2z - 16)}}{{z + 8}}$. . . . [Using Identity $IV]$
$ = \frac{{2z[z(z + 8) - 2(z + 8)]}}{{z + 8}}$
$ = \frac{{2z(z + 8)(z - 2)}}{{z + 8}}$
$= 2z (z – 2)$
$ = \frac{{4yz({z^2} + 6z - 16)}}{{2y(z + 8)}}$
$ = \frac{{2z({z^2} + 6z - 16)}}{{z + 8}}$
$ = \frac{{2z({z^2} + 8z - 2z - 16)}}{{z + 8}}$. . . . [Using Identity $IV]$
$ = \frac{{2z[z(z + 8) - 2(z + 8)]}}{{z + 8}}$
$ = \frac{{2z(z + 8)(z - 2)}}{{z + 8}}$
$= 2z (z – 2)$
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