Introduction to Factorisation

If $\frac{p}{q}+\frac{q}{p}=2,$ what is the value of ${\left(\frac{p}{q}\right)}^{23}+{\left(\frac{q}{p}\right)}^7$

Factorise $4\left(x+y\right)\left(3a-b\right)+6\left(x+y\right)\left(2b-3a\right)$

$12mn(n^2+6n-16) ÷ 2m(n+8)$

Area of square is $\frac{25}{98}{x}^4+\frac{5}{42}{x}^2+\frac{1}{18}$ .Find the expression of the length of the diagonal

Factorise the following:

$a^2+b^2+2ab+2bc+2ca$

Write the factors of $x^3+(a+b+c)x^2+(ab+bc+ca)x+abc$.

Solve: $L^2+L+\frac{1}{4}$

Factors of $2a^2+20ab+50b^2$ are:

Factorise the following expression by regrouping.

$q(r-s{)}^2+p(s-r)+3r-3s$

Factorise: $45ab{\left(a-b\right)}^2-15b{\left(a-b\right)}^3$

Factorise $x^2+13x-48$

Factorise:

$x\left(x+3\right)+5\left(x+3\right)$

$\left(a^2-b^2-4ac+4c^2\right)=$

Factorise: $2x\left(a-b\right)+3y\left(5a-5b\right)+4z\left(2b-2a\right)$

Factorise the following polynomial by taking out the H.C.F.

$10x^3{y}^2-14x^2{y}^3+28x{y}^4$

Factorise the following polynomial by taking out the H.C.F.

$8x^2-64xy+12x$

Factorise the following polynomial by taking out the H.C.F.

$a^4-4a^3+2a^2$

Factorise the following polynomial by taking out the H.C.F.

$20p{x}^{2}y-15qxy$

Which identity will be used to factorise $y^2-\frac{x^2}{100}$?

Factorise:

$16a^2-25b^2-8a+1$