Factorisation of Algebraic Expressions

The greatest common factor of the given monomials$14x^3{y}^3$, $21x^5{y}^2$, $35x^6{y}^6$ is $k{x}^3{y}^2$.  Find the value of $k$.

Factorising the following expression ${\left(ax+by\right)}^2-{\left(bx+ay\right)}^2$ we get $\left(x^2-y^k\right)\left(a^2-b^2\right)$, find the value of $k$.

Factorise the given expressions.

$ax-bx+by+cy-cx-ay$

Factorise the following expressions.

$ax+bx-ay-by+az+bz$

Factorise the given expression.

$2a{x}^2+3axy-2bxy-3b{y}^2$

Factorise the given expression.

$axy+bcxy-az-bcz$

On factorising $x^3-2x{y}^2-4y^3+2x^{2}y$ we get $\left(x+ky\right)\left(x^2-2y^2\right)$, find the value of $k$.

On factorising $2x^4-x^3+4x-2$ we get $\left(2x-k\right)\left(x^3+2\right)$, find the value of $k$.

On factorising the following expression $8-4x-2x^3+x^4$ we get $\left(2-x\right)\left(k-x^3\right)$, find the value of $k$.

Factorise the following expressions.

$a{b}^2-ab-a^{2}b+a^2$

On factorising the following expression $a{b}^2-b{c}^2-ab+c^2$ we get $\left(b-k\right)\left(ab-c^2\right)$, find the value of $k$

On factorising the following expression $15+x^{2}y+5y+3x^2$ we get $\left(y+3\right)\left(x^2+k\right)$, find the value of $k$.

On factorising the following expression $x^3+2x-2x^2-4$ we get $\left(x^2+k\right)\left(x-2\right)$, find the value of $k$.

On factorising the expression $a{x}^2+b{x}^2+2a+2b$ we get $\left(a+b\right)\left(x^2+k\right)$, find the value of $k$.

On factorising the following expressions $x^3-x^2+x-1$, we get $\left(x-k\right)\left(x^2+1\right)$, find the value of $k$

Factorise the given expression.

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

Factorise the given expression.

$p^{2}x-pqy+2px-2qy$

Factorise the given expression.

$2x^2+3xy-2xz-3yz$

Factorise the following expressions.

$x^2-x\left(a+2b\right)+2ab$

If the factorised form of $3+2xy+6x+y$ is $\left(ax+b\right)\left(cy+d\right)$, then write the value of $a+b+c+d$.