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Transcript of Foil
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Your Friend:
F.O.I.L
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A polynomial is an expression made with constants, variables and exponents, which are combined using addition, subtraction and multiplication, ... but not division.
Terms are made up of coefficients and/or variables.
x, 4, -2x, 3x2
Note: A polynomial expression with one term is called a monomial.
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Polynomial expressions with two terms are called binomials.
3x2 – 4x4, -11x7 + 9x13
We know how to combine like terms, and we know properties of exponents . . .So how would we expand a monomial times a binomial?
3x3 (4x2 – 5x)
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!3x3 (4x2 – 5x)
^ This monomial needs to be DISTRIBUTED to both terms within the binomial . . .
hmmm….
Distributive Property:a(b + c) = a(b) + a(c)a(b - c) = a(b) – a(c)
So, 3x3 (4x2 – 5x) = 3x3 (4x2) – 3x3(5x)
= 12x5 – 15x4
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Multiplying a binomial times a binomial also uses the Distributive Property. (x + 11)(x – 4)
Let m = (x + 11) n = x p = 4
Then we have m(n - p)…
Use the Distributive Property!
m(n - p) = m(n) – m(p)
Now substitute the original values back in…
(x + 11)(x) – (x + 11)(4)
The Distributive Property can be used again on
both pieces,
(x2 + 11x) – (4x + 44)
Now, drop the parentheses and combine like
terms:
x2 + 11x – 4x – 44 = x2 + 7x - 44
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We can shortcut some of the previous steps by using a helpful acronym.
F.O.I.L
(This acronym is NOT its own property, but a derivation of the Distributive Property!)
irst
uter
nner
ast
When multiplying two binomials, F.O.I.L reminds us how to multiply the terms within the binomials!
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Let’s try the previous problem, this time remembering F.O.I.L(x + 11)(x – 4)We do the steps of F.O.I.L in order:
“First” reminds us to multiply the first term in each binomial together.(x + 11)(x – 4)= x2
“Outer” reminds us to multiply the outermost terms together.(x + 11)(x – 4)= -4x
“Inner” refers to multiplying the innermost terms.(x + 11)(x – 4)= 11x
“Last” reminds us to multiply the last term in each binomial together.(x + 11)(x – 4)= -44
(x + 11)(x – 4) = x2 - 4x + 11x – 44
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That was much easier!
Remember, F.O.I.L can be used when multiplying any binomial by another binomial.