Adding and Subtracting Polynomials 6-4

Slides:



Advertisements
Similar presentations
Adding and Subtracting Polynomials 7-6
Advertisements

Warm Up Add Multiply (8) (22)
Simplifying Expressions
Warm Up Simplify each expression by combining like terms. 1. 4x + 2x 2. 3y + 7y 3. 8p – 5p 4. 5n + 6n 2 Simplify each expression. 5. 3(x + 4) 6. –2(t +
Simplifying Expressions
Simplifying Polynomials 14-2 Warm Up Identify the coefficient of each monomial. 1. 3x 4 2. ab –cb 3 Use the Distributive Property to simplify each.
A monomial is a number, a variable, or a product of numbers and variables with whole-number exponents. The degree of a monomial is the sum of the exponents.
Adding and Subtracting Polynomials 7-6
6-3 Polynomials Warm Up Lesson Presentation Lesson Quiz
7-5 Polynomials Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1.
7.5 P OLYNOMIALS & 7.6 A DDING AND S UBTRACTING P OLYNOMIALS Classify polynomials and write polynomials in standard form. Evaluate polynomial expressions.
Lesson 8-1 Warm-Up.
Multiplying Polynomials
3.1 Adding, Subtracting and Multiplying Polynomials 11/26/2012.
x4 1. x(x3) 2. 3x2(x5) 3x7 3. 2(5x3) 10x3 4. x(6x2) 6x3 5. xy(7x2)
= y 13 = -10d 7 = – 72a 33 b )5.) 6.)
Objectives The student will be able to: 1. add and subtract polynomials.
Adding and Subtracting Polynomials
Warm Up Simplify each expression by combining like terms. 1. 4x + 2x
Warm Up Simplify each expression by combining like terms. 1. 4x + 2x 2. 3y + 7y 3. 8p – 5p 4. 5n + 6n 2 Simplify each expression. 5. 3(x + 4) 6. –2(t.
Holt McDougal Algebra Simplifying Expressions Warm Up Add Multiply (8) (22)
Holt Algebra Simplifying Expressions Use the Commutative, Associative, and Distributive Properties to simplify expressions. Combine like terms. Objectives.
Algebra 1B Chapter 10 Polynomials and Factoring Adding and Subtracting.
CHAPTER Adding and subtracting polynomials.
Holt Algebra Simplifying Expressions 1-7 Simplifying Expressions Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz.
Adding and Subtracting Polynomials 1/6/2014. Example 1 Add Polynomials Vertically a. Add and 2x 32x 3 x9 + 4x 24x 2 + – x 3x 3 5x5x1 6x 26x 2 – + – 3x.
7-7 Adding and Subtracting Polynomials Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview.
Warm Up Combine like terms. 1. 9x + 4x 2. –3y + 7y 3. 7n + (–8n) + 12n
Warm Up Simplify each expression by combining like terms. 1. 4x + 2x 2. 3y + 7y 3. 8p – 5p 4. 5n + 6n 2 Simplify each expression. 5. 3(x + 4) 6. –2(t +
Holt Algebra Dividing Polynomials Warm Up Divide. 1. m 2 n ÷ mn x 3 y 2 ÷ 6xy 3. (3a + 6a 2 ) ÷ 3a 2 b Factor each expression. 4. 5x x.
Holt CA Course Adding Polynomials Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview.
SECTION 2.6 ADDING AND SUBTRACTING EXPRESSIONS OBJECTIVES: USE THE DISTRIBUTIVE PROPERTY TO COMBINE LIKE TERMS AND SIMPLIFY EXPRESSIONS WITH SEVERAL VARIABLES.
Adding and Subtracting Polynomials 6-4
Lesson 7.7 Adding and Subtracting Polynomials
Preview Warm Up California Standards Lesson Presentation.
Simplifying Expressions
6-3 Polynomials Warm Up Lesson Presentation Lesson Quiz
Adding and Subtracting Polynomials 7-6
Adding and Subtracting Polynomials 6-4
Simplifying Expressions
went to Poly- Nomial’s house to visit her Ma-Nomial who had a son,
Simplifying Expressions
Adding and Subtracting Polynomials 7-6
Adding and Subtracting Polynomials 6-4
Adding and Subtracting Polynomials
Objectives Use the Commutative, Associative, and Distributive Properties to simplify expressions.
7-5 Polynomials Lesson Presentation Lesson Quiz Holt Algebra 1.
Objectives Combining like terms..
Objectives Combining like terms..
Adding and Subtracting Polynomials 7-7
Lesson Objective: I will be able to …
To add or subtract polynomials, combine like terms.
Adding and Subtracting Polynomials 7-6
7-5 Polynomials Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1.
Adding and Subtracting Polynomials 6-4
Adding and Subtracting Polynomials 7-6
Simplifying Expressions
Adding and Subtracting Polynomials 7-7
Warm Up Simplify each expression by combining like terms. 1. 4x + 2x
Adding and Subtracting Polynomials 6-4
 .
Objectives Use the Commutative, Associative, and Distributive Properties to simplify expressions.
Adding and Subtracting Polynomials 6-4
Adding and Subtracting Polynomials 6-4
Adding and Subtracting Polynomials 6-4
Simplifying Expressions
Simplifying Expressions
Adding and Subtracting Polynomials 6-4
Adding and Subtracting Polynomials 7-6
Algebra 1 O.T.Q. Simplify each expression by combining like terms.
Presentation transcript:

Adding and Subtracting Polynomials 6-4 Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1 Holt Algebra 1

Warm Up 01/06/17 Simplify each expression by combining like terms. 1. 4x + 2x 2. 8p – 5p Simplify each expression. 3. 3(x + 4) 4. –1(x2 – 4x – 6)

Essential Objective Add and subtract polynomials.

Just as you can perform operations on numbers, you can perform operations on polynomials. To add or subtract polynomials, combine like terms.

Example: Adding and Subtracting Monomials A. 12p3 + 11p2 + 8p3 Identify like terms. 12p3 + 11p2 + 8p3 20p3 + 11p2 Combine like terms. B. 5x2 – 6 – 3x + 8 5x2 – 6 – 3x + 8 Identify like terms. 5x2 – 3x + 2 Combine like terms.

I do…. C. t2 + 2s2 – 4t2 – s2 t2 + 2s2 – 4t2 – s2 Identify like terms. t2 – 4t2 + 2s2 – s2 –3t2 + s2 D. 10m2n + 4m2n – 8m2n 10m2n + 4m2n – 8m2n Identify like terms. 6m2n

Like terms are constants or terms with the same variable(s) raised to the same power(s). Remember!

We d0.... Add or subtract. a. 2s2 + 3s2 + s 2s2 + 3s2 + s 5s2 + s b. 4z4 – 8 + 16z4 + 2 4z4 – 8 + 16z4 + 2 4z4 + 16z4 – 8 + 2 20z4 – 6

You do…. Add or subtract. c. 2x8 + 7y8 – x8 – y8 x8 + 6y8 d. 9b3c2 + 5b3c2 – 13b3c2 b3c2

Polynomials can be added in either vertical or horizontal form. In vertical form, align the like terms and add: In horizontal form, use the Associative and Commutative Properties to regroup and combine like terms. 5x2 + 4x + 1 + 2x2 + 5x + 2 7x2 + 9x + 3 (5x2 + 4x + 1) + (2x2 + 5x + 2) = (5x2 + 2x2) + (4x + 5x) + (1 + 2) = 7x2 + 9x + 3

Example: Adding Polynomials

To subtract polynomials, remember that subtracting is the same as adding the opposite. To find the opposite of a polynomial, you must write the opposite signs of each term: Change the signs and proceed to addition! –(2x3 – 3x + 7)= –2x3 + 3x – 7

Example: Subtracting Polynomials (x3 + 4y) – (2x3) Rewrite subtraction as addition of the opposite. (x3 + 4y) + (–2x3) (x3 + 4y) + (–2x3) (x3 – 2x3) + 4y –x3 + 4y Combine like terms.

We do…. Subtract. (–10x2 – 3x + 7) – (x2 – 9) (–10x2 – 3x + 7) + (–x2 + 9) (–10x2 – 3x + 7) + (–x2 + 9) –10x2 – 3x + 7 –x2 + 0x + 9 –11x2 – 3x + 16

You do…. Subtract. (9q2 – 3q) – (q2 – 5) (9q2 – 3q) + (–q2 + 5) (9q2 – 3q) + (–q2 + 5) 9q2 – 3q + 0 + − q2 – 0q + 5 8q2 – 3q + 5

Example: Application A farmer must add the areas of two plots of land to determine the amount of seed to plant. The area of plot A can be represented by 3x2 + 7x – 5 and the area of plot B can be represented by 5x2 – 4x + 11. Write a polynomial that represents the total area of both plots of land. (3x2 + 7x – 5) Plot A. + (5x2 – 4x + 11) Plot B. 8x2 + 3x + 6 Combine like terms.

Lesson Quiz 01/06/17 Add or subtract. 1. 7m2 + 3m + 4m2 2. (r2 + s2) – (5r2 + 4s2) 3. (10pq + 3p) + (2pq – 5p + 6pq) 4. (14d2 – 8) + (6d2 – 2d +1) 5. (2.5ab + 14b) – (–1.5ab + 4b)