Question

follow these steps to derive the law of cosines.

1. the relationship between the side lengths in $\triangle abd$ is

$c^{2}=x^{2}+h^{2}$ by the pythagorean theorem.

1. the relationship between the side lengths in $\triangle cbd$ is

$a^{2}=(b-x)^{2}+h^{2}$ by the pythagorean theorem.

1. the equation $a^{2}=(b-x)^{2}+h^{2}$ is to become

$a^{2}=b^{2}-2bx+x^{2}+h^{2}$.
correct
check

Explanation:

Step1: Identify algebraic operation

We expand $(b-x)^2$ using the binomial square formula $(m-n)^2 = m^2 - 2mn + n^2$.
$$(b-x)^2 = b^2 - 2bx + x^2$$

Step2: Substitute expanded form

Replace $(b-x)^2$ in $a^2=(b-x)^2+h^2$ with the expanded expression.
$$a^2 = b^2 - 2bx + x^2 + h^2$$

Answer:

expanded