Question

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 $c^2=h^2+b^2-2bx-x^2$

Answer 1

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Answer:

  B  c² = h² + b² -2bx +x²

Step-by-step 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