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In the proof of the Law of Cosines, the equation
c^2=h^2+(b-x)^2 was created using the Pythagorean theorem. Which equation is a result of expanding
(b-x)^2?

A
c^2=h^2+b^2-x^2
B
c^2=h^2+b^2-2bx+x^2
C
c^2=h^2+b^2+x^2
D
c^2=h^2+b^2-2bx-x^2

1 Answer

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Answer:

B c² = h² + b² -2bx +x²

Explanation:

The square of the binomial can be expanded using the distributive property:

c² = h² +(b -x)²

c² = h² +(b -x)(b -x)

c² = h² +b(b -x) -x(b -x)

c² = h² +b² -xb -bx +x²

c² = h² +b² -2bx +x² . . . . . matches choice B

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