The document provides instructions on multiplying polynomials. It discusses multiplying monomials by polynomials by distributing the monomial. It also covers multiplying binomials using the FOIL method, which involves multiplying the First, Outer, Inner, and Last terms. Finally, it addresses multiplying binomials by polynomials with more than two terms, which does not use FOIL but instead distributes the binomial to every term. Examples and practice problems are provided for each type of polynomial multiplication.

1. CHALLENGE
9
MULTIPLYING
POLYNOMIALS
1
Multiplying Polynomials
Goals
1) To multiply a _______________________by a ______________________.
2) To multiply more challenging __________________________.
3) To multiply a ______________________ by a ______________________. Algebra
Tiles
Using
algebra
tiles
can
help
you
visualize
problems.
This
set
of
tiles
shows
the
problem
Multiplying monomials and polynomials 2x(3x
+
1)
To multiply monomials by polynomials, you must _______________________
the monomial. For each term, multiply the _____________________ (the
numbers) and the _____________________ with the same ________________.
Remember, multiplying exponents with the same base means ______________________ the
________________________________.
Example Multiply monomials and polynomial.
Practice
6. 2x(2x3 + 4x – 4) 1. 4x(5x2 + x + 6)
7. 5b(2b2 + 7b – 3) 2. 5v3(2v2 + 7v – 3)
8. 4y(y2 + 7y – 2) 3. –2y(y4 + 7y3 – 5y2)
9. –3x(3x2 – 4x + 6) 4. –5x(2x2 – 6x + 10)
10. b(b3 + b2 – b) 5. d2(d4 + d3 – d2)
Multiplying binomials
To multiply two binomials, you must ___________________________ both ___________________
of the first binomial. The method for doing this is called _________________________.
Example Multiplying binomials.
Algebra
Tiles
This
set
of
tiles
shows
how
(x+5)(2x+1)
becomes
2x2
+
11x
+
5.

2. CHALLENGE
9
MULTIPLYING
POLYNOMIALS
2
Practice
6. (2y + 5)(y – 3) 1. (8w + 2)(w + 5)
7. (4b – 2)(b + 3) 2. (3c – 7)(2c + 5)
8. (8w + 2)(3w + 4) 3. (n2 + 2)(v + 6)
9. (5x – 4)(3x – 2) 4. (3x2 + 2)( x + 5x2)
10. (5a + 2)(5a – 1) 5. (5c + 7)(5c – 7)
Multiplying binomials by polynomials
To multiply a binomial with a larger polynomial, you must ___________________________ both
___________________ of the binomial to every term of the other polynomial. The FOIL method
doesn’t work with this type of multiplying because there are more than four terms.
Example Multiplying binomials by polynomials
Practice
6. (x + 2)(x2 + 6x + 4) 1. (2x + 3)(5x2 + 5x + 5)
7. (6n – 8)(2n2 + n + 7) 2. (n – 6)(4n2 + 3n + 2)
8. (b2 – 4)(b3 – b2 – b) 3. (4b3 – 7)(2b2 + 3b – 8b)
9. (3k2 + 3k)(5k2 + 6k + 8) 4. (k + 5)(k2 + 2k + 9)
10. (a – 4)(a2 – 2a + 1) 5. (2b – 7)(2b2 – 3a + 4)