Expand the following:
$\left(4-\frac{1}{3 x}\right)^{3}$
Expand the following:
$\left(4-\frac{1}{3 x}\right)^{3}$
We have,
$\left(4-\frac{1}{3 x}\right)^{3}=(4)^{3}-\left(\frac{1}{3 x}\right)^{3}-3(4)\left(\frac{1}{3 x}\right)\left(4-\frac{1}{3 x}\right)$
$\left[\because(a-b)^{3}=a^{3}-b^{3}-3 a b(a-b)\right]$
$=64-\frac{1}{27 x^{3}}-\frac{4}{x}\left(4-\frac{1}{3 x}\right)$
$=64-\frac{1}{27 x^{3}}-\frac{16}{x}+\frac{4}{3 x^{2}}$
Similar Questions
If the polynomial $a x^{3}+4 x^{2}+3 x-4$ and polynomial $x^{3}-4 x+a$ leave the same remainder when each is divided by $x-3,$ find the value of $a$.
If the polynomial $a x^{3}+4 x^{2}+3 x-4$ and polynomial $x^{3}-4 x+a$ leave the same remainder when each is divided by $x-3,$ find the value of $a$.
Find the following products:
$\left(x^{2}-1\right)\left(x^{4}+x^{2}+1\right)$
Find the following products:
$\left(x^{2}-1\right)\left(x^{4}+x^{2}+1\right)$
By Remainder Theorem find the remainder, when $p(x)$ is divided by $g(x),$ where
$p(x)=x^{3}-2 x^{2}-4 x-1, \quad g(x)=x+1$
By Remainder Theorem find the remainder, when $p(x)$ is divided by $g(x),$ where
$p(x)=x^{3}-2 x^{2}-4 x-1, \quad g(x)=x+1$
$x+1$ is a factor of the polynomial
$x+1$ is a factor of the polynomial
Evaluate
$(421)^{2}$
Evaluate
$(421)^{2}$