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Chapter 0: Problem 106

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Special-product formulas have patterns that make their multiplications quicker than using the FOIL method.

Short Answer

Expert verified
The statement makes partial sense. Special-product formulas do have patterns that can make their multiplications quicker than using the FOIL method but this is only applicable to specific patterns and not in general.

Step by step solution

01

Understand Special-Product Formulas

Special-product formulas are shortcuts used in algebra to quickly multiply two expressions of the form \( (a + b)(a - b) \), \( (a + b)^2 \), and \( (a - b)^2 \).
02

Understand the FOIL Method

The FOIL method is another way to multiply two binomials. The acronym FOIL stands for first, outer, inner, last, referring to the four multiplications that occur: multiply the first terms of each binomial, the outer terms, the inner terms, and lastly the last terms.
03

Compare the Two Methods

Comparing the two methods, the FOIL method involves a systematic way to perform four multiplications for any two binomials. On the other hand, special-product formulas, when applicable, can further simplify these multiplications. However, it is not generally quicker than the FOIL method but in certain cases with specific patterns, it can be quicker.

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