1.

Factorise each of the following:(i) `27 y^3+125 z^3` (ii) `64 m^3-343 n^3`

Answer» (i)`27y^3 + 125z^3`
`= 3^3y^3 + 5^3z^3`
`= (3y)^3 + (5z)^3`
using identity `a^3 + b^3 = (a+b)(a^2+b^2 -ab)`
`= (3y+5z)((3y)^2 + (5z)^2 -(3y)(5z))`
`= (3y+5z)(9y^2+25z^2 - 15yz)`
answer(ii) `64m^3 - 343n^3`
`= 4^3m^3 - 7^3n^3`
`= (4m)^3 - (7n)^3`
using identity `(a^3 - b^3) =(a-b)(a^2 + b^2 +ab) `
`= (4m-7n)((4m)^2 + (7n)^2 + (4m)(7n))`
`=(4m-7n)(16m^2 +49n^2 +28mn)`


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