MPM2D1 Date: _____________

Day 2: Multiplying Binomials

PART A - CLASSIFYING POLYNOMIALS

You can classify a polynomial by its number of terms or its degree.

1. NUMBER of TERMS

A monomial has just one term. For example: 4x2. Remember that a

term contains both the variable(s) and its coefficient (the number in front

of it.) So the is just one term.

A binomial has two terms. For example: 5x2 -4x

A trinomial has three terms. For example: 3y2+5y-2

Any polynomial with four or more terms is just called a polynomial.

For example: 2y5+ 7y

3- 5y

2+9y-2

2. NUMBER of DEGREE

The degree of the polynomial is found by looking at the term with

the highest exponent on its variable(s).

Examples:

5x2-2x+1 The highest exponent is the 2 so this is a 2

nd degree trinomial.

3x4+4x

2 The highest exponent is the 4 so this is a 4

th degree binomial.

8x-1 While it appears there is no exponent, the x has an

understood exponent of 1; therefore, this is a 1st degree binomial.

5 There is no variable at all. Therefore, this is a 0 degree

monomial. It is 0 degree because x0=1. So technically, 5 could be written

as 5x0.

3x2y

5 Since both variables are part of the same term, we must add

their exponents together to determine the degree. 2+5=7 so this is

a 7th

degree monomial.

http://padlet.com/Bulut/classifyingpolynomials

Mathematics Enhanced Scope and Sequence – Algebra I

Virginia Department of Education © 2011 2

Multiplying Polynomials Using Algebra Tiles Name Date

Use algebra tiles to model each multiplication problem and find the product. Draw your model in the frame. Write your simplified answer in the space provided.

1. x(x + 1) 2. 2x(x − 2) Answer:_______________ Answer:_______________ 3. x(2x + 2) 4. −x(x − 3) Answer:_______________ Answer:_______________

Mathematics Enhanced Scope and Sequence – Algebra I

Virginia Department of Education © 2011 3

5. (2x+ 1)(x + 1) 6. (−3x + 2)( −x − 2) Answer:_______________ Answer:_______________ 7. (2x + 1)(x − 4) 8. (−2x − 2)( 2x − 1) Answer:_______________ Answer:_______________

MPM2D1 Date: _______________

Day 2b: Multiplying Binomials – FOIL

3

Warm-Up:

If You Can Multiply: x (x + 2) = ______________________

And You Can Multiply: 3 (x + 2) = _______________________

Then You Can Multiply: (x + 3)(x + 2) How do you think you do this?

When multiplying 2 binomials, remember this acronym:

F -

O -

I -

L -

Basically:

multiply each term in the first bracket by each term in the second bracket

remember: when you multiply terms you multiply the coefficients and add the

exponents

collect like terms if applicable

Examples: Simplify (aka: expand and collect like terms)

))(( dcba

MPM2D1 Date: _______________

Day 2b: Multiplying Binomials – FOIL

4

a. (2x + 3)(x + 4) = b. (4x - 3)(2x - 1) =

c. (5 – 3z)(3z - 2) = d. (x + 4y)(3x - 5y) =

Now, let’s get more interesting:

e. (x - 5)2 = f. (2x + 3)2 =

Even more exciting:

g. 3(2x + 4y)2 = h. (x - 1)(3 - 2x) + (3x + 1)(2x - 1) =

MPM2D1 Date: _______________

Day 2b: Multiplying Binomials – FOIL

5

i. (2x + 3)2 - (3x + 4)(x - 2) =

j. A square has its length increased by 3cm and its width reduced by 5cm. Write an

expression for the new area.

Let x = the length of the original square

New length = _______________ New width = _______________

New area =

Play the game on the website below

http://bit.ly/multiplyingbinomials