### Instruction: Expand the product ${6(x+2)(x+3)}$.### Response: I notice that this is a product of three factors, and I can use the distributive property to expand it.
I can start by multiplying the first factor, 6, with the second factor, (x+2), using the distributive property.
That gives me ${6x+12}$.
Now I have to multiply this result by the third factor, (x+3), using the distributive property again.
That means I have to distribute both the 6x and the 12 to the x and the 3 in the third factor.
So I get ${(6x+12)(x+3) = 6x^2+18x+12x+36}$.
Simplifying the terms, I get ${6x^2+30x+36}$.
This is the expanded form of the original product.