Algebraic Identities

If $p=101$, then find the value of $\sqrt[3]{p\left(p^2-3p+3\right)-1}$.

What should come in the place of ($?$) for the expression given below?

$(y-z{)}^3+(z-x{)}^3+(x-y{)}^3=?$

If $a+\frac{1}{a}=\sqrt{3}$, find the value of $a^3+{\left(\frac{1}{a}\right)}^3$=?

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

If $x = 3 +2\surd 2$ ,then the value of ${ x }^{ 4 }+\cfrac { 1 }{ { x }^{ 4 } }$ is

${(a+b)}^2+{(b+c)}^2=$?

The expansion of $a^3$ is ___________ .

Evaluate ${99}^2$ by using suitable identity.

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

Where, $n$ is a positive number.

if $x+\frac{1}{x}=7$, then find $\frac{2x}{\left(3x^2+5x+3\right)}$.

If $\frac{p^2-q^2}{p+q}=50$, then $p-q=$_____

If${(a-b)}^2 + {(b-c)}^2 + {(c-a)}^2 = 0,$ then what is the value of $\cfrac { a+b }{ b+c } +\cfrac { a+c }{ a+b } +\cfrac { b+c }{ a+c }$

If $a+p – 2 = 0$, then the value of$a^2 + 6ap +p^3 – 8$ is ?

What should come in the place of ($?$) for the expression given below?

$\left(\sqrt{2}+\sqrt{7-2\sqrt{10}}\right)=?$

If ${\left(x+\frac{1}{x}\right)}^2=3$, then the value of $(x^{72} + x^{66} + x^{54} + x^{36} + x^{24} + x^6 + 1)$

If $a^2-b^2=21$ and $a^2+b^2=29$ which of the following could be the value of $ab$?

If $x-\frac{1}{x}=\sqrt{21}$ then find the value of $(x^2+\frac{1}{x^2})(x+\frac{1}{x})$will be

If$( x - a) (x - b) = 1$ and a - b + 5 = 0, then the value of ${\left(x-a\right)}^3-\frac{1}{{\left(x-a\right)}^3}$ is -

$x^4+4y^4$ is divisible by which one of the following?

If $x=19$ and $y=18$, then find the value of the expression $\frac{x^2+y^2+xy}{x^3-y^3}$ ?