Factorisation of Algebraic Expressions

Factorize the following algebraic expression:

$x^2-2xy-3y^2$.

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

The number of factors of $18$ is $5$.

Factorise $:(m-n{)}^8+(n-m{)}^7$

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

Factorise $:a(x-y)-b(y-x)$

Factorise $:(y+5)-3y(y+ 5)$

Factorise $:p(p-q)+q-p$

Factorise $:x(x-y)+2x-2y$

Factorise $:8p(4x+5y)-28q(4x+5y)$

Factorise $:10x(3a-4b)-15y(3a-4b)$

Factorise $:(p+q)r-(p+q)p$

Factorise $:a(x + y)+7(x + y)$