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. 2. the relationship between the side lengths in ( \triangle cbd ) is ( a^2 = (b - x)^2 + h^2 ) by the pythagorean theorem. 3. the equation ( a^2 = (b - x)^2 + h^2 ) is dropdown (options: expanded, factored, canceled) to become ( a^2 = b^2 - 2bx + x^2 + h^2 ). check button triangle diagram: a---d---c (base, length ( b )), d has right angle to b, ( ad = x ), ( dc = b - x ), ( bd = h ), ( ab = c ), ( bc = a )

Explanation:

Step1: Recall the formula for expanding a binomial square

The formula for expanding \((m - n)^2\) is \(m^2 - 2mn + n^2\). Here, in the expression \((b - x)^2\), we can let \(m = b\) and \(n = x\).

Step2: Apply the binomial expansion formula

Expanding \((b - x)^2\) using the formula \((m - n)^2=m^2 - 2mn + n^2\), we get \((b - x)^2=b^2-2bx + x^2\). So the equation \(a^2=(b - x)^2+h^2\) becomes \(a^2=b^2-2bx + x^2+h^2\) when we expand \((b - x)^2\).

Answer:

expanded