Problem 46 - College Algebra

Question

Find each product. $$(x-4)^{2}$$

Step-by-Step Solution

Answer

The product \( (x-4)^{2} \) simplifies to \( x^{2} - 8x + 16 \).

Step 1: Identify the Terms of the Binomial

The binomial is \( (x-4) \), so the first term (a) is x and the second term (b) is -4.

Step 2: Apply the Binomial Theorem

According to the Binomial Theorem for square terms, \( (a+b)^{2} = a^{2} + 2ab + b^{2} \). Now replace a and b with x and -4 respectively. Thus, \( (x-4)^{2} = x^{2} + 2*(-4)*x + (-4)^{2} \).

Step 3: Simplify the Expression

Let's simplify the expression derived from the previous step. \( x^{2} - 8x + 16 \).