Question

Factorise 8xcube-125ycube-27zcube-90xyz

Answer 1

Step-by-step explanation:

8x³-125y³-27z³-90xyz=(2x)³+(-5y)³+(-3z)³-3(2x)(-5y)(-3z)

We know that a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)

Here a=2x ; b=(-5y) ; c=(-3z)

8x³-125y³-27z³-90xyz=(2x + -5y + -3z)[(2x)²+(-5y)²+(-3z)²-(2xX-5y)-(-5yX-3z)-(2xX-3z)

=(2x-5y-3z)(4x²+25y²+9z²+10xy-15yz+6xz)

Answer 2

     

$Using the identity \ \ a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ac), \\ \\ \\ 8x^3-125y^3-27z^3-90xyz \\ \\ \Rightarrow\ (2x)^3+(-5y)^3+(-3z)^3-(3 \times 2x \times -5y \times -3z) \\ \\ \Rightarrow\ (2x-5y-3z)((2x)^2+(-5y)^2+(-3z)^2-(2x \times -5y)-(-5y \times -3z)-(2x \times -3z)) \\ \\ \Rightarrow\ (2x-5y-3z)(4x^2+25y^2+9z^2+10xy-15yz+6xz) \\ \\ \\ Hope this helps. \\ \\ Plz ask me if you've any doubts. \\ \\ \\ Thank you. :-))$