(a). The product of two binomials is sometimes called FOIL. It stands for ...
the product of the First terms (3j x 3j) plus the product of the Outside terms (3j x 5) plus the product of the Inside terms (-5 x 3j) plus the product of the Last terms (-5 x 5)
FOIL works for multiplying ANY two binomials (quantities with 2 terms).
Here's another tool that you can use for this particular problem (a). It'll also be helpful when you get to part-c .
Notice that the terms are the same in both quantities ... 3j and 5 . The only difference is they're added in the first one, and subtracted in the other one.
Whenever you have
(the sum of two things) x (the difference of the same things)
the product is going to be
(the first thing)² minus (the second thing)² .
So in (a), that'll be (3j)² - (5)² = 9j² - 25 .
You could find the product with FOIL, or with this easier tool. ______________________________
(b). This is the square of a binomial ... multiplying it by itself. So it's another product of 2 binomials, that both happen to be the same:
(4h + 5) x (4h + 5) .
You can do the product with FOIL, or use another little tool:
The square of a binomial (4h + 5)² is ...
the square of the first term (4h)² plus the square of the last term (5)² plus double the product of the terms 2 · (4h · 5) ________________________________
(c). Use the tool I gave you in part-a . . . twice .
The product of the first 2 binomials is (g² - 4) .
The product of the last 2 binomials is also (g² - 4) .
Now you can multiply these with FOIL, or use the squaring tool I gave you in part-b .
It is true that the quotient of two integers is always a rational number. This is because a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.
