Algebraic Identities

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

If $a^2 + b^2 = 117$ and $ab = 54$ , then $\frac{a+b}{a-b}$  is.

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 $x^2+\frac{1}{x^2}$?

Find the value of the question mark $\left(?\right)$.

$If b = -3 and a = 2 then a^2 + b^2 + 2ab = ?$

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

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

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

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

${\left(\sqrt{2}+\frac{1}{\sqrt{2}}\right)}^2=?$

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 $\mathrm{a}-\mathrm{b}=\sqrt{2}$ and $a+b=\sqrt{3}$  , then the value of $4ab ( a^2 + b^2)$ is

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 $a + b + c = 0$ , then what is the value of $\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}$?

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?

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