Applications of Identities

Factorise: $x^6-64$

Factorize:

$64x^3-27y^3-144x^{2}y+108x{y}^2$

Factorize:

$27x^3-\frac{1}{216}-\frac{9}{2}{x}^2+\frac{1}{4}x$

Expand:

${\left[\frac{1}{3}x+\frac{1}{5}z\right]}^3$

Expand:

${\left[\frac{1}{2}x-\frac{1}{3}y+\frac{1}{4}z\right]}^2$

Find the value of $\frac{0.125+0.64}{0.25+0.16-0.2}$

Find the value of $\frac{{\left(14.5+6.23\right)}^2-{\left(14.5-6.23\right)}^2}{\left(14.5\times 6.23\right)}$

If $x-\frac{1}{x}=-1$, find the value of $x^2+\frac{1}{x^2}+100$.

If $x+\frac{1}{x}=11$, find the value of $x^2+\frac{1}{x^2}+100$.

Find the value of the following expression $9x^2-24xy+16y^2$, when $x=\frac{2}{3}$ and $y=\frac{3}{4}$.

Find the value of the following expression $4x^2+12xy+9y^2$, when $x=\frac{5}{2}$ and $y=\frac{2}{3}$.

If $\left(a-\frac{1}{a}\right)=7$, then find the value of $a^2+\frac{1}{a^2}$.

Find the value of ${111}^2+{112}^2+{113}^2-111\times 112-112\times 113-113\times 111$

Find the value of $3.{29}^3+6.{71}^3$.

Expansion of ${\left(5{\mathrm{a}}^2+6{\mathrm{b}}^2\right)}^2$ is

Find: $\frac{55\times 55-40\times 40}{55+40}$

If $\left(x-y\right)=5$ and $xy=6$, then the value of $x^2+y^2$ is

If $x+\frac{1}{x}=3$, then the value of $x^2+\frac{1}{x^2}$ is

If $\left(x+y\right)=5$ and $xy=6$, find the value of $x^2-y^2$.

If $\left(x+y\right)=9$ and $xy=14$, find the value of $x^2-y^2$.