Answer:
x^2 +10x + 21
Step-by-step explanation:
You know the distributive property tells you ...
a(b +c) = ab +ac
Here, you can let
and you get ...
a ( b + c ) = a·b + a·c
(x +3)(x +7) = (x +3)·x +(x +3)·7
Now, you can use the distributive property on each of those products:
= x·x +3·x +x·7 +3·7
= x^2 +10x + 21
_____
Alternate solution
This is perhaps more commonly done by separating the terms of the first factor first:
(x +3)(x +7) = x(x +7) +3(x +7)
Then the next round looks like ...
x^2 +7x +3x +21
In order, left to right, these terms are the products of First terms, Outer terms, Inner terms, and Last terms. The acronym FOIL is often used to help students remember these pairs of products.
The acronym FOIL is only useful when multiplying a pair of binomials.
For anything else, the distributive property is relatively easy to remember and apply. Each term in each factor is multiplied by the remaining factors. The process is repeated until there are no parentheses left. Then like terms can be collected.
