Introduction to Identities

If $12x-15y=9x+5y$, the value of $\frac{x^2+y^2}{x^2-y^2}$ is

If$p=999$, then the value of  $\sqrt[3]{p(p^2+3p+3)+1}$ _____.

Out of the given responses, one of the factors is$x^3–3x^2+3x+7$ is -

If $x+\frac{1}{9x}=1$, then what is the value of $27x^3+\frac{1}{27x^3}$?

If $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0$ and$x^2+y^2+z^2=25$ , than the value of $x+y+z$ is/are?

If $x+\frac{1}{x}=\sqrt{13}$, then value of $x^3+\frac{1}{x^3}$ is:

If $x^{\frac{1}{3}}+y^{\frac{1}{3}}+z^{\frac{1}{3}}=0$, then what is ${\left(x+y+z\right)}^3$ is equal to

If $x^2+\frac{1}{x^2}=27$, find the value of $3x^3+5x-\frac{3}{x^3}-\frac{5}{x}$

If $a^3+\frac{1}{a^3}=52$, then the value of $2(a+\frac{1}{a})$ is:

$8a^3-125b^3$ when divided by $4a^2+10ab+25b^2$ gives 

Using the identity $a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)$, factorise:

$128x^3+54$

Using the identity $a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)$, factorise:

$27y^3+125z^3$

Try to write the value of $\frac{x^6-1}{x^3}$ if $\frac{x^2-1}{x}=2$.

${\left(a-b\right)}^3=$

Expand the expression $(1-3x{)}^3$

Simplify $\frac{x^3}{x-y}+\frac{y^3}{y-x}$

Simplify: ${\left(7x+y\right)}^3-{\left(7x-y\right)}^3$

Simplify: $(y+1{)}^3+(y-1{)}^3$

Factorise:  $225p^{12}-9q^6$

Simplify:

 ${\left(7x+y\right)}^3-{\left(7x+y\right)}^2$