Question

Factorise polynomial
27y3 + 125z3

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Answer 1

`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)`