Factorise $: 8 x^{3}+y^{3}-27 z^{3}+18 x y z$
Factorise $: 8 x^{3}+y^{3}-27 z^{3}+18 x y z$
$8 x^{3}+y^{3}-27 z^{3}+18 x y z$
$=(2 x)^{3}+(y)^{3}+(-3 z)^{3}-3(2 x)(y)(-3 z)$
$=\{2 x+y+(-3 z)\}\left\{(2 x)^{2}+(y)^{2}+(-3 z)^{2}-(2 x)(y)\right.$$-(y)(-3 z)-(-3 z)(2 x)\}$
$=(2 x+y-3 z)\left(4 x^{2}+y^{2}+9 z^{2}-2 x y+3 y z+6 z x\right)$
Similar Questions
For the polynomial
$\frac{x^{3}+2 x+1}{5}-\frac{7}{2} x^{2}-x^{6},$ write
$(i)$ the degree of the polynomial
$(ii)$ the coefficient of $x^{3}$
$(iii)$ the coefficient of $x^{6}$
$(iv)$ the constant term
For the polynomial
$\frac{x^{3}+2 x+1}{5}-\frac{7}{2} x^{2}-x^{6},$ write
$(i)$ the degree of the polynomial
$(ii)$ the coefficient of $x^{3}$
$(iii)$ the coefficient of $x^{6}$
$(iv)$ the constant term
Factorise the following:
$9 x^{2}-12 x+3$
Factorise the following:
$9 x^{2}-12 x+3$
Find the quotient and the remainder when $x^{3}+x^{2}-10 x+8$ is divided by
$x+3$
Find the quotient and the remainder when $x^{3}+x^{2}-10 x+8$ is divided by
$x+3$
Find the following product :
$(2 x-y+3 z)\left(4 x^{2}+y^{2}+9 z^{2}+2 x y+3 y z-6 x z\right)$
Find the following product :
$(2 x-y+3 z)\left(4 x^{2}+y^{2}+9 z^{2}+2 x y+3 y z-6 x z\right)$
Verify whether $3$ and $5$ are zeros of the polynomial $x^{2}-x-6$ or not.
Verify whether $3$ and $5$ are zeros of the polynomial $x^{2}-x-6$ or not.