Question

$\text{Factorise the expression:}-16y^{2}z+20z^3$

• A. $4z(y^2+5z^2)$
• B. $4z(4y^2+5z^2)$
• C. $4z(-4y^2-5z^2)$
• D. $4z(-4y^2+5z^2)$

Answer 1

The correct option is D $4z(-4y^2+5z^2)$

$\text{Given, the expression is}-16y^{2}z+20z^3.$

$\text{On factorizing the terms individually,}16y^{2}z=2\times 2\times 2\times 2\times y\times y\times z20z^3=2\times 2\times 5\times z\times z\times z$

$\text{The common factors are}2,2andz.$

$\text{Therefore,}-16y^{2}z+20z^3$
$=(-2\times 2\times 2\times 2\times y\times y\times z)+(2\times 2\times 5\times z\times z\times z)=(2\times 2\times z)[-(2\times 2\times y\times y)+(5\times z\times z\left)\right]=4z(-4y^2+5z^2)$