Dave F. answered • 04/08/14

Math and Excel Tutor - elementary school up to middle school subjects

^{2}

^{2 }-3x -36.

LaVonne C.

asked • 04/08/14whats the difference between foiling and distributing?

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Dave F. answered • 04/08/14

Tutor

New to Wyzant
Math and Excel Tutor - elementary school up to middle school subjects

"Foiling" IS distributing.

The FOIL method is used to multiply binomials, or to multiply (x + 3) by (3x -12) for example.

But FOILing can ONLY be used with binomials. Let find out why:

FOILing means first multiplying the FIRST terms together, or x and 3x to get 3x^{2}

Then multiply the OUTSIDE terms together, or x and -12 to get -12x.

Then multiply the INSIDE terms together, or 3 and 3x to get 9x.

The multiply the LAST terms together, or 3 and -12 to get -36.

Simplify by adding like terms to get 3x^{2 }-3x -36.

If we were to use distribution to multiply (x + 3) by (3x -12) we'd multiply x by 3x.

Then multiply x by -12.

Then multiply 3 by 3x.

Then multiply 3 by -12.

So FOILing IS distributing, but one cannot use the FOIL method on anything else but binomials.

i.e. we can't use the FOIL method to find the product of a trinomial and an binomial.

Steve S. answered • 04/08/14

Tutor

5
(3)
Tutoring in Precalculus, Trig, and Differential Calculus

f(n) = (4n+3)(4n+2)(4n+1)(4n)(4n-1)(4n-2)

FOIL quickly fails you.

But here’s an example of using the Distributive Property in a methodical way that provides error checking as you go:

http://www.wyzant.com/resources/answers/30917/simplify_the_expression

Jon B. answered • 04/08/14

Tutor

4.6
(58)
Math Minor - Tutors in math, especially algebra and statistics

The foil method is best used when the expression is in the form (x+a)*(x+b), where a and b are numbers. In this case, you need to go x*x + xa +xb + ab.

Distribution would be when there is only one term in one of the parenthesis, such as in the case of x*(x+3), in which case, it would be x*x + x*3.

(x+4)(x-3) = x^2 + x - 12 << FOIL

x*(x+3) = x^2 + 3x << Distribution

(x+4)(x-3) = x^2 + x - 12 << FOIL

x*(x+3) = x^2 + 3x << Distribution

Parviz F.

I just avoid FOIL all together, it is just useless memorization of irrelevance:

Multiply 2 binomial

( X + a ) ( X +b)

Just distribute it twice:

( X +a) X + b( X +a) = X ^2 + aX + bX + ab

Then factor by Grouping:

X^2 + ( a + b ) X + ab

Then it comes useful in factoring Quadratic and solving for roots

f( X) = X ^2 + ( a + b ) X + ab = ( X +a ) ( X +b )

f( x ) = 0 ( X +a ) = 0 X_{1} = -a ( X +b) = 0 X_{2} = -b

Substituting back ( X_{1 }, X_{2 ) into f( X)}

f( X) = X^2 - ( X_{1 }+ X _{2 ) X + X}_{1X2 } (2)

Equation (2) leads us to solution of roots of quadratic.

Where aX^2 + bX + c = 0

always X_{1} + X_{2 = - b/a } X_{1 }
. X_{2= c/a} (3)

Relationship ( 3) is the key Principle that leads to the solution of quadratic and even polynomial'

that should be emphasized instead of FOIL.

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04/08/14

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