Answer: The required multiplied form is [tex]a^3-216.[/tex]
Step-by-step explanation: We are given to multiply the following polynomials :
[tex]P=(a-6)(a^2+6a+36)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be using the following formula :
[tex](x-y)(x^2+xy+y^2)=x^3-y^3.[/tex]
From (i), we get
[tex]P\\\\=(a-6)(a^2+6a+36)\\\\=(a-6)(a^2-a \times6+6^2)\\\\=a^3-6^3\\\\=a^3-216.[/tex]
Thus, the required multiplied form is [tex]a^3-216.[/tex]
