Multiplying by a Monomial

Be able to multiply two monomials or a monomial and a polynomial

FHS Polynomials 2

Property 1 of Exponents

• Let’s look at an example that demonstrates how this property ____________ works:

• We have the problem: • According to the property we should be able

to find the answer this way:• We know that and

• Which gives us the same answer. 2 3 5a a a aa a a a

2a a a

2 3a a

m n m na a a

2 2 53 3a a a a 3a a a a

FHS Polynomials 3

Multiplying Monomials

• Unlike adding and subtracting, you can multiply any two monomials, even if they are not like terms.

• Simply multiply the coefficients together, and add the exponents of each set of different variables.

• Examples: (4x2)(-5x4) = (2x2y)(3x4y2) =

-20x6 6x6y3

(42)(44) = (x2)(x4y5) =

46 x6y5

FHS Polynomials 4

Multiplying a Polynomial by a Monomial

• To multiply a polynomial by a monomial, you must multiply each term in the polynomial by the monomial. For example:

1. 4(q – 5) multiply both q and 5 by the 4 4 · q – 4 · 5 = 2. (–5x)(5x – 4) = 3. (–3p2)(11p2 + 6pq + 12q2) =

4q – 20–25x2 + 20x

–33p4 – 18p3q – 36p2q2

FHS Polynomials 5

Problems from WS 3

1.

2.

11.

12.

15.

3x y

2 2a a

2 2e f e f

3 213 2mn m n

2 27 2x x xy y