Introduction to Factorisation

Factorize the following polynomial: $32{\mathrm{x}}^4-500\mathrm{x}$.

Factorisation of $16p^4+168p^3-88p^2$ is $k{p}^2\left(4p-2\right)\left(p+11\right)$

Find the value of $x-y$.

If $a^3+a=a\left(a^2+k\right)$ then find the value of $k.$

The number of factors of $18$ is $5$.

Reduce the equation $x\left(2x+1\right)=6$ to quadratic equation and find its roots.

Reduce the equation $x=\frac{3x+1}{4x}$ to quadratic equation and find its roots.

Reduce the equation $\frac{1}{x+1}+\frac{2}{x+2}=\frac{4}{x+4}$ to quadratic equation and find its roots.

Reduce the equation $\frac{2}{x^2}+\frac{17}{x}+21=0$ to quadratic equation and find its roots.

Factorise$:ab(x^2+y^2)-xy(a^2+b^2)$

Factorise $:y^2-xy(1-x)-x^3$

Factorise $:x^3+xy(1-2x)-2y^2$

Factorise $:a^3+9a^2+ab+9b-a-9$

Factorise $:x^3-x^2+ax+x-a-1$

Factorise $:6ax-4xy+9ay- 6y^2$

Factorise$:xy-pq-py+xq$

Factorise $:6xy-35-15x+14y$

Factorise $:ax-5b-bx+5a$

Factorise $:(m-n{)}^8+(n-m{)}^7$

Factorise$:15p(2x+3y{)}^3-10q(2x+3y{)}^2+25(2x+3y)$