multiplying binomials
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Multiplying Binomials
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ObjectiveI will be able to:
multiply two binomials by applying the
properties of operations to multiply two-digit
numbers (e.g.
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What is a binomial?- an algebraic expression of the sum or the difference of two terms
So how can we write 23 as a binomial?
Well….
Then 37 can be written as…37=30+7=3 𝑥+7
Then substitute 2x for 20 so, 3
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So
(2 𝑥+3 ) (3𝑥+7 )
Then, how do we multiply these two binomials?
The Distributive Property!
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Remember!3 𝑥 (4 𝑥−5)
^ This monomial needs to be DISTRIBUTED to both terms within the binomial . . .
Distributive Property: a(b + c) = a(b) + a(c)
Or a(b - c) = a(b) – a(c)
Thus, (5)
=
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Multiplying a binomial times a binomial also uses the Distributive Property.
(2 𝑥+3 ) (3𝑥+7 )
¿¿¿6 𝑥2+14 𝑥+9 𝑥+21
¿6 𝑥2+23 𝑥+21
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Let’s check our work….
If
¿6 𝑥2+23 𝑥+21𝑎𝑛𝑑 𝑥=10
⇒ 6 (10 )2+23 (10 )+21
⇒ 6(100)+23 (10 )+21⇒ 600+230+21⇒ 851
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Compare the results….
x 37
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We can use an acronym to help us remember the steps.
F-irst termsO-uter termsI-nner termsL-ast terms
(The acronym FOIL is NOT its own property, but a derivation of the Distributive Property!)
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Let’s try the another problem, this time remembering FOIL(x + 11)(x – 4)We do the steps of FOIL in order:
“First” reminds us to multiply the first term in each binomial together.(x + 11)(x – 4),
“Outer” reminds us to multiply the outermost terms together.(x + 11)(x – 4),
“Inner” refers to multiplying the innermost terms.(x + 11)(x – 4),
“Last” reminds us to multiply the last term in each binomial together.(x + 11)(x – 4),
So, (x + 11)(x – 4) = x2 - 4x + 11x – 44Combine like terms => x2 + 7x – 44
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Practice with where
(1𝑥+7 ) ( 4 𝑥+2 )
¿¿¿ 4 𝑥2+2𝑥+28 𝑥+14
¿ 4 𝑥2+30𝑥+14714
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That was much easier!
Remember, FOIL can be used when multiplying any binomial by another binomial.