Multiplying Binomials

ObjectiveI will be able to:

multiply two binomials by applying the

properties of operations to multiply two-digit

numbers (e.g.

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

So

(2 𝑥+3 ) (3𝑥+7 )

Then, how do we multiply these two binomials?

The Distributive Property!

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)

=

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

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

Compare the results….

x 37

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!)

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

Practice with where

(1𝑥+7 ) ( 4 𝑥+2 )

¿¿¿ 4 𝑥2+2𝑥+28 𝑥+14

¿ 4 𝑥2+30𝑥+14714

That was much easier!

Remember, FOIL can be used when multiplying any binomial by another binomial.