Algebra 1 Ch 2.6 – The Distributive Property. Objective Students will use the distributive property.
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Algebra 1 Ch 2.6 The Distributive Property Slide 2 Objective Students will use the distributive property Slide 3 Before we begin The distributive property is a key algebraic concept that looks something like this: 3(x + 4) We will work with this property and its many forms throughout this course It is expected that you are able to recognize and know how to work with this property If you cannot recognize and work with the distributive property you will not be successful in this course Slide 4 The Distributive Property The distributive property states: To multiply a number by a sum or difference, multiply each number inside the parentheses by the number outside the parentheses The distributive property can be used with multiplication and addition or multiplication and subtraction Lets see what it looks like Slide 5 Example 1 5(3 + 2) Proof: 5(3+2) = 5(5) = 25 15 + 10= 25 Slide 6 Algebraic Expressions The distributive property can be used to re-write algebraic expressions. Use the same processmultiply whats on the outside of the parenthesis by each term within the parenthesis Lets see what that looks like Slide 7 Example 2 Note: In this instance 3x and 3 are not like terms. Therefore, you cannot combine themso the expression is simplified to just 3x + 3 more on this later in the lesson 3(x + 1) + 33x Slide 8 Distributive Property There are 2 ways that you can see the distributive property With the multiplier on the left of the parenthesis With the multiplier on the right of the parenthesis Example: 5(2 + 3)OR(b + 3)5 In either event you multiply whats on the out side of the parenthesis with EACH term inside the parenthesis Slide 9 Comments AgainThe distributive property is a key algebraic conceptmake no mistake about ityou are REQUIRED to be able to recognize and work with the distributive property if you are to pass Algebra 1! Slide 10 Common Errors The most common error that students make when working the distributive property is that they only multiply what on the outside of the parenthesis with the first term within the parenthesis The other common error is that students get the signs wrongI do not give partial credit for incorrect signs! Slide 11 Example - Common Error THIS IS INCORRECT! 3(x - 1) - 13x Slide 12 Combining Like Terms In this course you will be expected to simplify expressions by combining like terms In order to do that you have to be familiar with the vocabulary and know the definition of combining like terms Lets take a look at that Slide 13 Vocabulary Term is the product of a number and a variable. (product means to multiply) Examples: 3xThree times x 3x 2 Three times x squared -xNegative 1 times x -xy 2 Negative 1 times x times y squared Slide 14 Vocabulary Coefficient the coefficient of a term is the number in front of the variable. If there is no number then the coefficient is positive 1. If there is no number and the variable is negative then the coefficient is -1. Examples: -3x-3 is the coefficient x1 is the coefficient -y-1 is the coefficient 5y 2 5 is the coefficient Slide 15 Vocabulary Like terms are terms that have the same variable and exponent. They can be combined by adding or subtracting. Examples: same variable raised to the same power. They can be combined by adding to get 8x 5x + 3x 5x 2 3x 2 same variable raised to the same power. They can be combined by subtracting to get 2x 2 5x + 3y Different variables raised to the same power they cannot be combined 5x 2 3x 4 Same variable raised to different powers they cannot be combined Slide 16 Vocabulary Constants a number with no variable is called a constant. Constant terms can be combined by adding or subtracting. Examples: 5x + 3 - 2 The constant terms are +3 and 2. They can be combined to get 5x + 1 - 7 + 6y - 2 The constant terms are 7 and 2. They can be combined to get 6y 9 Slide 17 Simplified Expressions An expression is considered simplified if it has no grouping symbols and all the like terms have been combined Example: -x 2 + 5x - 4 - 3x + 2 - x 2 cannot be combined with anything because there is no other squared term + 5x and 3x can be combined because they have the same variable and exponent to get +2x - 4 and + 2 are constant terms and can be combined to get 2. The simplified expression is: -x 2 + 2x- 2 Slide 18 Comments On the next couple of slides are some practice problemsThe answers are on the last slide Do the practice and then check your answersIf you do not get the same answer you must question what you didgo back and problem solve to find the error If you cannot find the error bring your work to me and I will help Slide 19 Your Turn Use the distributive property to rewrite the expression without parenthesis 1. 3(x + 4) 2. - (y 9) 3. x(x + 1) 4. 2(3x 1) 5. (2x 4)(-3) Slide 20 Your Turn Simplify by combining like terms 6. 15x + (-4x) 7. 5 x + 2 8. 4 + a + a 9. 8b + 5 3b 10. 9x 3 2 4x 3 Slide 21 Your Turn Apply the distributive property then simplify by combining like terms 11. (3x + 1)(-2) + y 12. 4(2 a) a 13. - 4(y + 2) 6y 14. -x 3 + 2x(x x 2 ) 15. 4w 2 w(2w 3) Slide 22 Your Turn Solutions 1. 3x + 12 2. -y + 9 3. x 2 + x 4. 6x 2 5. -6x + 12 6. 11x 7. 7 - x 8. 4 + 2a 9. 5b + 5 10. 5x 3 2 11. -6x 2 + y 12. 8 5a 13. -10y 8 14. -x 3 + x 2 15. 2w 2 + 3w Slide 23 Summary A key tool in making learning effective is being able to summarize what you learned in a lesson in your own words In this lesson we talked about the distributive property Therefore, in your own words summarize this lessonbe sure to include key concepts that the lesson covered as well as any points that are still not clear to you I will give you credit for doing this lessonplease see the next slide Slide 24 Credit I will add 25 points as an assignment grade for you working on this lesson To receive the full 25 points you must do the following: Have your name, date and period as well a lesson number as a heading. Do each of the your turn problems showing all work Have a 1 paragraph summary of the lesson in your own words Please be advised I will not give any credit for work submitted: Without a complete heading Without showing work for the your turn problems Without a summary in your own words