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Chapter 0: Problem 46

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

Short Answer

Expert verified
The product is \(x^2 - 8x + 16\).

Step by step solution

01

Represent the binomial squared

First of all, express the binomial squared as \((x-4)(x-4)\). This makes it easier to see the multiplication that needs to occur.
02

Apply FOIL

Now apply the FOIL method. Multiply the First terms (\(x*x = x^2\)), the Outer terms (\(x*-4 = -4x\)), the Inner terms (\(-4*x = -4x\)), and finally the Last terms (\(-4*-4 = 16\)).
03

Combine like terms

Combine the terms to get the final answer. The two middle terms (\(-4x\) and \(-4x\)) add up to \(-8x\). So, the final answer is \(x^2 - 8x + 16\).

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