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PowerPoint Overview Unit 1 Lesson 1.1 – Simplifying Expressions

Choctaw High School Algebra I EOI Review. PowerPoint Overview Unit 1 Lesson 1.1 – Simplifying Expressions. To simplify an algebraic expressions, you need to combine the like terms. Like terms have the same variables with the same exponents.

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PowerPoint Overview Unit 1 Lesson 1.1 – Simplifying Expressions

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  1. Choctaw High School Algebra I EOI Review PowerPoint OverviewUnit 1 Lesson 1.1 –Simplifying Expressions

  2. To simplify an algebraic expressions, you need to combine the like terms. Like terms have the same variables with the same exponents. If two terms are like terms, then only their coefficients may differ. Once you find all the like terms, you can combine them by adding or subtracting the coefficients only. Simplifying Expressions

  3. An algebraic expression is a collection of real numbers, variables, grouping symbols and operation symbols. Here are some examples of algebraic expressions. Algebraic Expressions

  4. The terms of the expression are separated by addition. There are 3 terms in this example and they are . The coefficientof a variable term is the real number factor. The first term has coefficient of 5. The second term has an unwritten coefficient of 1. The last term , -7, is called a constant since there is no variable in the term. Consider the example:

  5. Let’s begin with a review of two important skills for simplifying expression, using the Distributive Property and combining like terms. Then we will use both skills in the same simplifying problem.

  6. a ( b + c ) = ba + ca Distributive Property To simplify some expressions we may need to use the Distributive Property Do you remember it? Distributive Property

  7. Examples Example 1: 6(x + 2) Distribute the 6. 6 (x + 2) = x(6) + 2(6) = 6x + 12 Example 2: -4(x – 3) Distribute the –4. -4 (x – 3) = x(-4) –3(-4) = -4x + 12

  8. Try the Distributive Property on -7 ( x – 2 ) . Be sure to multiply each term by a –7. -7 ( x – 2 ) = x(-7) – 2(-7) = -7x + 14 Notice when a negative is distributed all the signs of the terms in the ( )’s change. Practice Problem

  9. Examples with 1 and –1. Example 3: (x – 2) = 1( x – 2 ) = x(1) – 2(1) = x - 2 Notice multiplying by a 1 does nothing to the expression in the ( )’s. Example 4: -(4x – 3) = -1(4x – 3) = 4x(-1) – 3(-1) = -4x + 3 Notice that multiplying by a –1 changes the signs of each term in the ( )’s.

  10. Like terms are terms with the same variables raised to the same power. Hint: The idea is that the variable part of the terms must be identical for them to be like terms. Like Terms

  11. Examples Like Terms 5x , -14x -6.7xy , 02xy The variable factors are identical. Unlike Terms 5x , 8y The variable factors are not identical.

  12. Recall the Distributive Property a (b + c) = b(a) +c(a) To see how like terms are combined use the Distributive Property in reverse. 5x + 7x = x (5 + 7) = x (12) = 12x Combining Like Terms

  13. All that work is not necessary every time. Simply identify the like terms and add their coefficients. 4x + 7y – x + 5y = 4x – x + 7y +5y = 3x + 12y Example

  14. Collecting Like Terms Example

  15. This example requires both the Distributive Property and combining like terms. 5(x – 2) –3(2x – 7) Distribute the 5 and the –3. x(5) - 2(5) + 2x(-3) - 7(-3) 5x – 10 – 6x + 21 Combine like terms. - x+11 Both Skills

  16. Simplifying Example

  17. Distribute. Simplifying Example

  18. Distribute. Simplifying Example

  19. Distribute. Combine like terms. Simplifying Example

  20. Distribute. Combine like terms. Simplifying Example

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