Proving and Applying Polynomial Identities
Algebra · Flashcards · Recall
ALGEBRA · FLASHCARDS
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QUESTION
What is the identity for
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
(a-b)(a^2+ab+b^2)
(
a
−
b
)
(
a
2
+
ab
+
b
2
)
?
QUESTION
What identity factors a difference of squares:
a
2
−
b
2
a^2-b^2
a
2
−
b
2
?
QUESTION
What identity verifies
(
m
2
−
n
2
)
2
+
(
2
m
n
)
2
=
(
m
2
+
n
2
)
2
(m^2-n^2)^2+(2mn)^2=(m^2+n^2)^2
(
m
2
−
n
2
)
2
+
(
2
mn
)
2
=
(
m
2
+
n
2
)
2
?
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ANSWER
(
x
2
+
y
2
)
2
=
(
x
2
−
y
2
)
2
+
(
2
x
y
)
2
(x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2
(
x
2
+
y
2
)
2
=
(
x
2
−
y
2
)
2
+
(
2
x
y
)
2
. The identity that validates all Pythagorean triple formulas.
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