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?

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

The value of $\left(1+\frac{1}{\mathrm{a}}\right)\left(1+\frac{1}{\mathrm{a}+1}\right)\left(1+\frac{1}{\mathrm{a}+2}\right)\left(1+\frac{1}{\mathrm{a}+3}\right)\left(1+\frac{1}{\mathrm{a}+4}\right)$ _____.

The value of $\frac{{\left(0.013\right)}^3+{\left(0.007\right)}^3}{{\left(0.013\right)}^2-0.013\times 0.007+{\left(0.007\right)}^2}$ is _____.

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

If $x=2+\sqrt{3,} y=2-\sqrt{3},$ then the value $\frac{x^2+y^2}{x^3+y^3}$ is _____.

What is the value of $\text{k}$ that $(2\mathrm{x}-1)$ may be a factor of $4{\mathrm{x}}^4-(\mathrm{k}-1){\mathrm{x}}^3+{\mathrm{kx}}^2-6\mathrm{x}+1$ ?

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

If ${\mathrm{a}}^2+{\mathrm{b}}^2+{\mathrm{c}}^2–\mathrm{ab}–\mathrm{bc}–\mathrm{ca}=0$, then _____.

If $\frac{{\left(x-y\right)}^2}{x^2-y^2}=9$ then, the value of $\frac{{\displaystyle \frac{x}{y}}+1}{{\displaystyle \frac{x}{y}}-1}$ is __________.

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

A basket has$x$ mangoes, how many mangoes are there in $5$ baskets?

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

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

If $x=\frac{2\sqrt{10}}{7}$ then, find the value of $\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}$.

The expression for the statement: $y$multiplied by $10$ and then $7$ added to product.

The value of $\frac{1-{\mathrm{x}}^4}{1+\mathrm{x}}÷\frac{1+{\mathrm{x}}^2}{\mathrm{x}}\times \frac{1}{\mathrm{x}\left(1-\mathrm{x}\right)}$is ______.

If  $\sqrt{1+\frac{\mathrm{x}}{9}}=\frac{13}{3}$ then the value $\mathrm{x}$ is ______.

If $({\mathrm{x}}^4+{\mathrm{x}}^{-4})=322$, what is one of the values of $(\mathrm{x}-{\mathrm{x}}^{-1})$?

If $tan\theta +\frac{1}{tan\theta }=2$, then what is the value of $ta{n}^2\left(\theta \right)+\frac{1}{ta{n}^2\left(\theta \right)}$?