Algebraic Identities

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

$(-a-b{)}^2=$

Expand ${\left(\frac{3a}{8}-14b\right)}^2$

If ${\left(a+b+c\right)}^2= 3\left(ab+bc+ca\right)$, then which one of the following is true?

The value of ${\left(x-y\right)}^3+{\left(x+y\right)}^3+3{\left(x-y\right)}^2\left(x+y\right)+3{\left(x+y\right)}^2\left(x-y\right)$ is:

If ${\left(x+y\right)}^2-z^2=18, {\left(y+z\right)}^2-x^2=52$ and ${\left(z+x\right)}^2-y^2=30$, then select the value of $\left(x+y+z\right)$.

Find the value of  $x^3+\frac{1}{x^3}$, if value of $x= 7-4\sqrt{3}$.

Factorise: $1-49(x+y{)}^2$

Expand: ${\left(a+b\right)}^2$

Find: $\frac{55\times 55-40\times 40}{55+40}$

If $\left(x-y\right)=5$ and $xy=6$, then the value of $x^2+y^2$ is

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

If two expressions are equal for all the values of same parameter, then the statement of equality between the two expressions is called an identity.

Check whether given one is identity or equation?

${\left(\mathrm{a}+\mathrm{b}\right)}^2={\mathrm{a}}^2+2\mathrm{ab}+{\mathrm{b}}^2$

If $\left(x+y\right)=5$ and $xy=6$, find the value of $x^2-y^2$.

If $\left(x+y\right)=9$ and $xy=14$, find the value of $x^2-y^2$.

If $x-\frac{1}{x}=4$, find the value of $x^4+\frac{1}{x^4}$

If $x-\frac{1}{x}=4$, find the value of $x^2+\frac{1}{x^2}$

The product of $\left(x+2y\right)\left(x-2y\right)\left(x^2+4y^2\right)$ is $x^4-p{y}^4$, find the value of $p$.

The product of $\left(x+y\right)\left(x-y\right)\left(x^2+y^2\right)$ is $x^p-y^q$, find the vlaue of $p+q$