Prove polynomial identities and use them to describe numerical relationships.

Sample Practice Questions (3)

The polynomial identity

(x^{2} + y^{2})^{2} = (x^{2} - y^{2})^{2} + (2 x y)^{2}

can be used to generate Pythagorean triples. If

x = 3

and

y = 2

, which set of numbers represents the resulting Pythagorean triple?

5, 12, 13

3, 4, 5

9, 4, 13

7, 24, 25

A square has a side length of

a + b

. Its area can be represented by the identity

(a + b)^{2} = a^{2} + 2 ab + b^{2}

. If the square is divided into four regions as shown in the diagram, which region represents the

2 ab

portion of the identity?

ATwo rectangles each with area

ab

BA single square with area

a^{2}

CA single square with area

b^{2}

DFour small squares each with area

0.5 ab

The identity

(x^{2} - y^{2})^{2} + (2 x y)^{2} = (x^{2} + y^{2})^{2}

can be used to generate Pythagorean triples. If

x = 3

and

y = 2

, what are the lengths of the three sides of the resulting right triangle?

5, 12, 13

3, 4, 5

9, 4, 13

7, 24, 25

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