Proving and Applying Polynomial Identities
Geometry · Flashcards · Recall
GEOMETRY · FLASHCARDS
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QUESTION
What is the expansion of
(
a
−
b
)
3
(a-b)^3
(
a
−
b
)
3
?
QUESTION
In $
(
x
2
+
y
2
)
2
(x^2+y^2)^2
(
x
2
+
y
2
)
2
=
(
x
2
−
y
2
)
2
(x^2-y^2)^2
(
x
2
−
y
2
)
2
+
(
2
x
y
)
2
(2xy)^2
(
2
x
y
)
2
$, what is the common hypotenuse expression?
QUESTION
Which condition on
m
m
m
and
n
n
n
guarantees a primitive Pythagorean triple from Euclid's formula?
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ANSWER
gcd
(
m
,
n
)
=
1
\text{gcd}(m,n)=1
gcd
(
m
,
n
)
=
1
and
m
,
n
m,n
m
,
n
have opposite parity. Ensures the triple has no common factors.
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