Expansions Using Algebraic Identities

If $\left(x-\frac{1}{x}\right)=4$, then find the value of  $8\left(x^2+\frac{1}{x^2}\right)$

What is square of 213

Find: ${\left(m+2n+3r\right)}^2$

Find all $x, y\in N$; $x, y\le 100$ and $\frac{1}{x}+\frac{4}{y}=\frac{1}{12}$ and $y$ is odd.

$\left(a^3-8\right)÷\left(a-2\right)$

Evaluate: $12\times 12+13\times 13+14\times 14$

Evaluate: $2a+5a=$_____

Expand: ${\left(K+G\right)}^3$

if $x-\frac{1}{x}=\sqrt{6}$ then $x^2+\frac{1}{x^2}=$?.

If $2x+3y=13, xy=6$, find the value of $8x^3+21y^3$

If $x+y+z=8$ and $xy+yz+zx=20$, find the value of $x^3+y^3+z^3-3xyz$.

Simplify the following expressions: ${\left(2x+3y+4z\right)}^2+{\left(x+\frac{y}{2}+\frac{z}{3}\right)}^2-{\left(\frac{x}{2}+\frac{y}{3}+\frac{z}{4}\right)}^2$

Simplify $\left(\frac{1}{2}a-3b\right)\left(3b+\frac{1}{2}a\right)\left(\frac{1}{4}{a}^2+9b^2\right)$

If $x+\frac{1}{x}=11$, find the value of $x^2+\frac{1}{x^2}$

Identify the terms and factors of $1+x+x^2$ and show them in tree diagram.

State whether the following statement is true or false.

On the number line, the position of a number $-9$ lies on the right-hand side of the origin.

State whether the following statement is true or false.

On the number line, the position of a number $5$ lies on the right-hand side of the origin.

Evaluate:

$9^{-\frac{1}{2}}$

From the given tree diagram, write the expression.

Tree diagrams are used to identify the terms and factors of an algebraic expression.