Question

factorise x^3-343y^3+512z^2+168xyz​

Answer 1

Answer:

(x-7y+8z) (x²+49y²+64z²+7xy+56yz-8zx)

Step-by-step explanation:

Let F=x³-343y³+512z³+168xyz​

F=x³+(-7y)³+(8z)³-3*(x)*(-7y)*(8z)

let x=a, -7y=b, and 8z=c

Then F=a³+b³+c³-3abc

We know that

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

Hence F=(a+b+c)(a²+b²+c²-ab-bc-ca)

putting value of a,b, c

F=(x-7y+8z)[ x²+(-7y)²+(8z)²-x(-7y)-(-7y)(8z)-x(8z) ]

=(x-7y+8z) (x²+49y²+64z²+7xy+56yz-8zx)