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Chapter 0: Problem 49

Find each product. $$(7-2 x)^{2}$$

Short Answer

Expert verified
The multiplication of \( (7-2x)^2 \) results in \( 4x^2 -28x + 49 \)

Step by step solution

01

Understand the Squaring of Binomial

When you see \( (7-2x)^2 \), remember that it means \( (7-2x) * (7-2x) \). Do not make the common mistake of simply squaring each term individually, instead you should do the actual multiplication operation.
02

Apply FOIL Method

FOIL stands for First, Outer, Inner, and Last, which is a method for multiplying binomials. For our specific problem, the FOIL method would look like this: First: 7*7 = \( 49 \). Outer: 7*(-2x) = \( -14x \). Inner: -2x*7 = \( -14x \). Last: -2x*-2x = \( 4x^2 \). So the intermediate result by adding all these together gives \( 49 - 14x -14x + 4x^2 \).
03

Simplify the Result

Combine like terms from the intermediate result. This gives \( 49 -28x + 4x^2 \). Since the degree of \( x^2 \) is the highest, by convention, we write it at the front, so our polynomial becomes: \( 4x^2 -28x + 49\).

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