a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)

Formula use:

\left(a+b\right)^2=a^2+2ab+b^2

#### Explanation

Given expression is: 8\left(x+y\right)^3-{27\left(y+z\right)}^3 *Factorize*

8\left(x+y\right)^3-{27\left(y+z\right)}^3

\rightarrow\{2\left(x+y\right)\}^3-\{3\left(y+z\right)\}^3

\rightarrow\left(2x+2y\right)^3-\left(3y+3z\right)^3

\rightarrow\left(2x+2y-3y-3z\right)\{\left(2x+2y\right)^2+\left(2x+2y\right).\left(3y+3z\right)+\left(3y+3z\right)^2\}

\rightarrow\left(2x-y-3z\right)\left({4x}^2+8xy+{4y}^2+6xy+{6y}^2+6xz+6yz+9y^2+18yz+9z^2\right)

\therefore\left(2x-y-3z\right)\left({4x}^2+14xy+19y^2+6xz+24yz+9z^2\right) **Ans:** \left(2x-y-3z\right)\left({4x}^2+14xy+19y^2+6xz+24yz+9z^2\right)