FOIL Strategies
As the examples in the previous section reveal, you can proceed methodically when you multiply binomial terms. The most universally adopted method in this respect is identified with the acronym FOIL (First, Outer, Inner, and Last). Figure 8.3 illustrates how the FOIL approach to multiplication works.
Figure 8.3. The FOIL approach allows you to work more effectively with multiplication of binomials.
As an example of the application of the FOIL technique of multiplying binomials, consider this problem:
(m + 4)(m2 + 9)
F O I L
= m (m2)+ m (9)+ 4(m2)+ 4(9)
= m3 + 9m + 4m2 + 36
Figure 8.4 illustrates the relationships that exist between the values generated using the FOIL approach and the areas of a rectangle that represent the values.
Figure 8.4. A set of rectangles allows you to visualize the FOIL approach.
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