Identities

If $\mathrm{X}=2+\sqrt[3]{2}+{\left(\sqrt[3]{2}\right)}^2$, then find the value of ${\mathrm{X}}^3-6{\mathrm{X}}^2+6\mathrm{X}$.

Given$t=2+\sqrt[3]{4}+\sqrt[3]{2},$find the value of$t^3-6t^2+6t-2.$

If ${\left(x+\frac{1}{x}\right)}^2=3,$ then the value of $x^{206}{+x}^{200}+x^{90}+x^{84}{+x}^{18}+x^{12}{+x}^6+1$ is _____.

Find the product of: [by using identity]  $\left(2.5x^6+0.2y^5\right)\left(2.5x^6+0.2y^5\right)$

Solve equation, $x-4=3$.

Find the algebraic identity ${\left(a+b\right)}^2$.

Prove: $a^2-b^2=(a+b)(a-b)$

Solve ${\left(3x+5\right)}^2$.

If $a+b=10, ab=6$ Then find $a^2-ab+b^2$

$(2a+3{)}^2-(2a-3{)}^2$

Factorise $4y^2-12yz+9z^2$

$\frac{x-2}{x+2}+\frac{x+2}{x-2}=4$

Hemlata says, ‘the length of the diagonal of the painting along with the border is $2\left(\sqrt{\frac{l^2}{2}-l+1}\right)$. Is Hemlata correct? Justify your answer.

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

$(a+b)$ whole square

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

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

Simplify: $20-4x-2x+2=0$

Divide $(x²-4) \text{by} (x+2)$

Simplify:

$\frac{x^2-{\left(y-z\right)}^2}{{\left(x+z\right)}^2-y^2}+\frac{y^2-{\left(x-z\right)}^2}{{\displaystyle {\left(x+y\right)}^2}{\displaystyle -}{\displaystyle {{\displaystyle z}}^2}}+\frac{z^2-{\left(x-y\right)}^2}{{\displaystyle {\left(y+z\right)}^2}{\displaystyle -}{\displaystyle {{\displaystyle x}}^2}}$