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

9514 1404 393

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