Manipur Board Solutions for Chapter: Factorisation, Exercise 1: EXERCISE 3.1

Factorise $a(b+c{)}^2+b(c+a{)}^2+c(a+b{)}^2-3abc$.

Factorise $8(a+b+c{)}^3-(b+c{)}^3-(c+a{)}^3-(a+b{)}^3$.

Prove that $(x-y{)}^3+(y-z{)}^3+(z-x{)}^3-3(x-y\left)\right(y-z\left)\right(z-x)=0$.

If $a^3+b^3+c^3=3abc$, prove that either $a+b+c=0$ or $a=b=c$.

If $x+y+z=9, xy+yz+zx=26$ and $xyz=24$, find the value of $x^2(y+z)+y^2(z+x)+z^2(x+y)$.

If $x+y-z=2, y+z-x=4$ and $z+x-y=6$, find the value of $2y^2{z}^2+2z^2{x}^2+2x^2{y}^2-x^4-y^4-z^4$.

If $x+y+z=12$ and $x^2+y^2+z^2=44$, find the value of $(x+y+z{)}^3-x^3-y^3-z^3+3xyz$.

Find the value of $xy(x+y)+yz(y+z)+zx(z+x)+3xyz$, when $x=a(b-c), y=b(c-a), z=c(a-b)$.