Algebraic Identities

If $a+b+c=0$, then the value of $\left(\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}\right)$ is:

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 $\left(a^2-b^2\right)\sin \left(\theta \right)+2ab\cos \left(\theta \right)=a^2+b^2$, then what is the value of $\tan \left(\theta \right)$?

If $a+b+c=0$ then $\frac{a^2+b^2-c^2}{ab}$ is equal to _____.

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 _____.

If $2x-\frac{1}{2x}=6$, then what is the value of $x^2+\frac{1}{16x^2}$?

If ${\left(x+\frac{1}{x}\right)}^2=3$. then the value of $x^{206}+x^{200}+x^{90}+x^{84}+x^{12}+x^6+1$ is _____.

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?

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

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

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.