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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Special Products

• The so-called FOIL method of multiplying two binomials is nothing more than a special case of multiplying polynomials. The acronynm FOIL stands for First, Outside, Inside, and Last.
• When multiplying the sum and difference of two terms, the FOIL method leads to the two middle terms cancelling out.}

Example:

Use FOIL to multiply (2x + 3)(2x - 3)

Shortcut (Product of the Sum and the Difference of Two Terms)

( A + B )( A - B) = A 2 - B 2.

Any binomial in the form A 2 is called a difference of squares .

• When squaring a binomial, one must remember to FOIL and NOT JUST SQUARE EACH TERM .

Example:

Compute (5a - 2) 2

Shortcut (Squaring a Binomial)

( A + B ) 2 = A 2 + 2AB + B 2

( A - B ) 2 = A 2 - 2AB + B 2

• None of the formulae in this section are strictly needed to succeed in algebra. They are shortcuts, and nothing else. You will not be tested on them, but they can save you a lot of time if you know how to use them properly.