Answer:
Option (d) is correct.
[tex]c^2 = h^2+(b - x)^2=h^2+b^2+x^2-2bx[/tex]
Step-by-step explanation:
Given : in the proof of the Law of Cosines, the equation [tex]c^2 = h^2+(b - x)^2[/tex] was created using the Pythagorean theorem.
We have to write the equation in expanded form by expanding [tex](b - x)^2[/tex] and choose the correct option
Consider the given equation [tex]c^2 = h^2+(b - x)^2[/tex]
We will expand [tex](b - x)^2[/tex] using algebraic identity
[tex](a-b)^2=a^2+b^2-2ab[/tex]
Here a= b and b = x
On simplify we get,
[tex](b - x)^2=b^2+x^2-2bx[/tex]
Thus equation becomes,
[tex]c^2 = h^2+(b - x)^2=h^2+b^2+x^2-2bx[/tex]
Thus, option (d) is correct.
