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EXTRA

FOIL

When working with quadratic equations, you will often need to FOIL. FOIL is the process you use to get from factored form to standard form of a quadratic equation. Anytime you are multiplying two terms that both have a plus or minus, you need to FOIL when distributing the numbers. FOIL stands for: First, Outside, Inside, Last.

Let’s say we want to change (y=(x-3)(x+1)) from factored form into standard form. Here’s how we would FOIL:

First, we multiply the first part of each term: ((x)(x) = x^2). Then, we multiply the two inside parts: ((-3)(x)=(-3x)). Then, we multiply the two outside parts: ((x)(1)=x). Then, we multiply the last part of each term: ((-3)(1)=(-3)). Finally, we add all of those amounts together and simplfly:

(x^2 – 3x + x – 3)
(x^2 – 2x -3)

Practice

Practice using FOIL to change the equations from factored form into standard from:

(y=(x-5)(x+6))

(y=(x+5)(x+2))

(y=(x-4)(x-4))

Perfect Squares/Difference of Squares

A perfect square occurs when you multiply a binomial factor times itself. Let’s say we want to factor the equation (y=x^2+16x+64). We can see that (8+8=16), and ((8)(8)=64), so the factored form of the equation would be (y=(x+8)(x+8)). We could also write that as: (y=(x+8)^2).

Occasionally on the SAT, you will also need to know difference of squares. This occurs when you multiply a binomial factor times the same binomial factor with an opposite sign. For example, let’s say we need to FOIL (y=(x+4)(x+4)). We would get (y=x^2+4x-4x-16). The (4x-4x) cancel each other out and leave us with (y=x^2-16).

When you see an equation like (y=x^2-) (a single term), you are dealing with a difference of squares problem.

The difference of squares formula is: ((a-b)(a+b) = a^2-b^2)

Traps

The hidden FOIL
When finding an equivalent value for a perfect square like ((x+ 3)^2), students often incorrectly put (x^2+9). You still need to FOIL. Re-write the problem as: ((x+ 3)(x+ 3)), then FOIL to get the correct answer: (x^2+6x+9).