circles are 360⁰ and lines are 180⁰
(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.
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(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)
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(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 .
Answer:
D is the answer
Step-by-step explanation:
just divide 17 by 6 and you'll get your mixed number:
2 5/6
The set of two-digit primes is {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}
Of that list, the following primes are mirror images of each other
13 and 31
17 and 71
37 and 73
79 and 97
Note: we ignore 11 since 11 flips to 11 which is not distinct from its original
If you're looking for the largest prime of this form, then its 97
If you're looking for the largest gap, then subtract each pair
31-13 = 18
71-17 = 54
73-37 = 36
97-79 = 18
We see that 71 and 17 have the largest gap
