addition and subtraction of...

adding and subtracting polynomials_collecting like terms.notebook

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March 19, 2013

Addition and Subtraction of Polynomials

Teachers' notesLesson objectives

1) Students will be able to identify degree of both a term and polynomial.

2) Students will be able to identify like terms within an expression. 3) By the end of the lesson students will be able to add and subtract simple polynomials.


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Lesson objectives Teachers' notes

Teacher:

Subject:

Topic:

Grade(s):

Prior knowledge:

MPM 1D MFM 1P

Adding and Subtracting Polynomials

Grade 9

addition and subtraction of integers andlike and unlike terms

Maria Morris

Lesson notes:Students should be familiar with the use of algebra tiles, and it would be beneficial for each student or a pair of students to have a package of tiles to work with throughout lesson. The homework assigned on the last page of lesson is for the MPM and is from McGraw Hilland Ryerson, "Principles of Mathematics 9".

ExpectationsMPM 1D• manipulate numerical and polynomial expressions,• add and subtract polynomials with up to two variables [e.g., (2x – 5) + (3x + 1), (3x2y + 2xy2) + (4x2y – 6xy2)], using a variety of tools (e.g., algebra tiles, computer algebra systems, paper and pencil);MFM IP• simplify numerical expressions involving integers and rational numbers, with and without the use of technology;• add and subtract polynomials involving the same variable up to degree three [e.g.,(2x + 1) + (x2 – 3x + 4)], using a variety of tools (e.g., algebra tiles, computer algebra systems, paper and pencil);


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Julio says that the term x2 has a coefficient of 2 and a variable x. Is Julio correct? Explain.


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Are these expressions equivalent? Explain.

a) 2w + 1t and 2w + t

b) 3x + 1 and 3x

Explain when you must write the number 1, and when you do not need to.


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Addition & Subtractionof

Polynomials(Collecting Like Terms)


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What is a like term?

Like terms are terms that have identical variables. Therefore, they have the same variable with the same exponent on the variable.

Examples:


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Polynomials should be written in standard form. This means that the powers of the

variables should go from the highest exponent to the lowest exponent.

Ex. 4x 3 + 3x2 -8x + 6


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Only like terms can be combined when adding or subtracting polynomials. Therefore, you are collecting like terms. They MUST contain

the same variable and exponent or they are not like terms and therefore can not be combined.

Ex. Only x 2 terms can be combined with other x 2 terms. Therefore, x2 and

x cannot be combined because they don'tfit the rule for like terms. There are thesame variable but not the same exponent.

So How Do We Add/Subtract Polynomials?


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Algebra Tiles can help us to visualize how to add/subtract polynomials by combining

like terms:

If an algebra tile is WHITE, then the sign of the term is NEGATIVE. However, if it is any other color, then the sign of the term is POSITIVE.

Therefore, when adding a WHITE tile with a COLORED tile of the SAME term, the result

will be zero, and they will cancel each other out.

x2

x2

1

1

x

x

y

y

y2

y2


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A polynomial can be represented using algebra tiles.

4x 2 -2x + 5

x

xx2 x2 1

1

Now drag the algebra tiles to represent the polynomial 4x 2 -2x + 5.

x2x2 x2 x2

xx

1 11

11


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Let's try modeling some polynomials by dragging the algebra tiles:

3x 2 -2x + 4

1 1x2x2 xx

x2x2

x2

xx

11 1

1


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Now model: x 2 +3x -2

x 2 +3x -2

11x2x2 x

x

x2

x

xx

1

1


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Now, let's add the two polynomials we just represented:

(3x 2 -2x + 4) + (x 2 + 3x -2)

2x 2

x2

xx x 1

1

11

x x1

1

x

2x

Let's have a volunteer come up to group our like terms together

+


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After combining like terms, our algebra tiles should look like this:

2x

2x

2x

1 1

2x

1 1

x x

xx1 1

x

We need another volunteer to come up to cancel out our positive and negative

like terms.


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After canceling, our algebra tiles should look like this:

2x

2x

2x

1 1

2x

x

Can you write the polynomial that is now represented after we added:(3x 2 -2x + 4) + (x 2 + 3x -2)?

If you calculated 4x 2 + x + 2, you're right!

Give yourself a hand!


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Now, let's subtract:(3x 2 -2x + 4) - (x 2 + 3x -2)

Now, that our first polynomial is represented we need to take away the 2nd one from the 1st. Any Volunteers??

1 1x2x2 x

x

Start by dragging tiles out to represent the first polynomial.

x2 x2

x2

x

x1 1

11x

xx

x

x

x

1

1

11

11 1

1


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x2 x2

xxxxx

11

111 1

After subtracting and combining like terms, our algebra tiles should look like this:

Can you write the polynomial that is now represented after we subtracted:

(3x 2 -2x + 4) - (x 2 + 3x -2)?

If you calculated 2x 2 - 5x + 6, you're right!

Give yourself a hand!


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Now it's time for you to practice adding and subtracting some polynomials by yourselves. Remember to use your algebra tiles if you

get stuck. There are also more examples in your textbook in the pages that precede your homework questions.

So now go to your textbook pg 151-152 #1-8, 10


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