Algebraic Identities

On simplification $(3+\sqrt{3})(3-\sqrt{3})$ gives:

Find the value of $\frac{(237+12{)}^2-(237-12{)}^2}{237\times 12}$

Which of the following is the correct expansion of $(\mathrm{x}+\mathrm{y}+\mathrm{z}{)}^2?$

Factorise, $\left(b+c-a\right)\left(c+a-b\right)\left(a+b-c\right)+8abc$

Factorise, $\left(a^2-b^2\right)\left(a+b\right)+\left(c^2-a^2\right)\left(c+a\right)+\left(b^2-c^2\right)\left(b+c\right)$

Factorise, $a^4\left(b^2-c^2\right)+b^4\left(c^2-a^2\right)+c^4\left(a^2-b^2\right)$

Factorise, $b^2{c}^2\left(b^2-c^2\right)+c^2{a}^2\left(c^2-a^2\right)+a^2{b}^2\left(a^2-b^2\right)$

Factorise, $a{\left(b+c\right)}^2+b{\left(c+a\right)}^2+c{\left(a+b\right)}^2-4abc$

Factorise, $bc\left(b^3-c^3\right)+ca\left(c^3-a^3\right)+ab\left(a^3-b^3\right)$

If $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}=0$, then find $\left[{\left(\frac{x}{y}\right)}^3+{\left(\frac{y}{z}\right)}^3+{\left(\frac{z}{x}\right)}^3\right]$
 

If $x^3-k{x}^2+4=\left(x+1\right){\left(x-a\right)}^2$ be an identity, then find the value of $k$ and $a$
 

The product of $(a+8)(a+8)$ is $a^2+16a+64$. (Use the appropriate identity)

Find the value of ${10}^3-{\left(5\right)}^3-{\left(5\right)}^3$.

Find the value of $x^3+\frac{1}{x^3}$, if $x+\frac{1}{x}=2$

Using appropriate identity, find the product of $102\times 98$.

Find the value of $x^2+\frac{1}{x^2}$, if $x-\frac{1}{x}=1$

$104\times 96=$?

Find the value of $27x^3+8y^3$, if $3x+2y=20$ and $xy=\frac{11}{9}$.

Find the value of $x^2+\frac{1}{x^2}$, if $x-\frac{1}{x}=\sqrt{3}$.