Question

Factorise polynomial 27y3 + 125z3​

Answer 1

Answer:

$27y^{3} +125z^{3} =(3y)^{3} +(5z)^{3}$

Apply the formula for sum of cubes: $a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})$

Therefore:

$\left(3y\right)^3+\left(5z\right)^3=\left(3y+5z\right)\left(3^2y^2-3\cdot \:5yz+5^2z^2\right)$

$=\left(3y+5z\right)\left(9y^2-15yz+25z^2\right)$