6.2 Multiplying polynomials

We use the acronym below to multiply two binomials.

F – O – I – L –

FIRSTOUTSIDEINSIDELAST

1. 2.

2x−3( ) 5x+ 3( ) 7x3 + 5( ) x2 −2( )

1. The product of the sum and difference of two terms.

2. The square of a binomial sum.

3. The square of a binomial difference.

x + y( ) x−y( ) =

x + y( )2 =

x−y( )2 =

3. 4.

4y + 3( ) 4y−3( ) 3x + 7( )2

Multiply each term of one of the polynomials by each term of the other, and then add all the monomial products.

It may be helpful to line up the common terms vertically.

5. 2x−1( ) x2 −4x+ 3( )

6. 3x−2( ) 5x4 −x3 + 4x( )

To cube a binomial, write the binomial times. FOIL two binomials and then multiply the resulting trinomial by the remaining binomial.

three

7. x−2( )3

8. x + 4( )3

Multiplication works the same for multiple variables as it does for one variable, just make sure to only combine terms.

like

9. 3c + 5d( )2

10. a + 2b( ) 3a2 −ab−7b2( )