Factorise $m^2-4mn-21n^2$.

Factorise $6x^2+19x+15$.

Factorise $12x^2+7x-12$.

Factorise $6x^2-23xy+20y^2$.

If $\left(4x^2+5x-7\right)+\left(-3x^2+3x-4\right)+ \left(x^2-1\right)=a{x}^2+bx-12$ then find the value of $a+b$.

If $\left(3y^2-2xy+x^2\right)+\left( 5x^2+4xy-3y^2\right)+\left(4xy-2x^2\right)=a{x}^2+bxy$ then find the value of $a+b$.

Multiply $3x^2+4xy+y^2$ by $2x+4y$.

Multiply $\left(x+1\right)\left(x^2-xy-y^2\right)$.