Simplifying expressions
- 1. Simplifying Expressions By Zain Bin Masood Senior Maths Teacher At The Intellect School
- 2. Objective This presentation is designed to give a brief review of simplifying algebraic expressions and evaluating algebraic expressions.
- 3. Algebraic Expressions An algebraic expression is a collection of real numbers, variables, grouping symbols and operation symbols. Here are some examples of algebraic expressions. 1 5 5 x + x −7 , 4 , xy − , 3 7 2 −7( x −2 )
- 4. Consider the example: 5 x + x − 7 2 The terms of the expression are separated by addition. There are 3 terms in this example and they are 5x 2 , x , − 7 . The coefficient of 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.
- 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. Distributive Property To simplify some expressions we may need to use the Distributive Property Do you remember it? Distributive Property a ( b + c ) = ba + ca
- 7. Examples Example 1: 6(x + 2) Distribute the 6. Example 2: -4(x – 3) Distribute the –4. 6 (x + 2) = x(6) + 2(6) = 6x + 12 -4 (x – 3) = x(-4) –3(-4) = -4x + 12
- 8. Practice Problem 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.
- 9. Examples with 1 and –1. Example 3: (x – 2) Example 4: -(4x – 3) = 1( x – 2 ) = -1(4x – 3) = x(1) – 2(1) = 4x(-1) – 3(-1) =x - 2 = -4x + 3 Notice multiplying by a 1 does nothing to the expression in the ( )’s. Notice that multiplying by a –1 changes the signs of each term in the ( )’s.
- 10. Like Terms 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.
- 11. Examples Like Terms 5x , -14x Unlike Terms 5x , 8y -6.7xy , 02xy − 3 x y , 8 xy The variable factors are identical. The variable factors are not identical. 2 2
- 12. Combining Like Terms 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
- 13. Example 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
- 14. Collecting Like Terms Example 4 x 2 −13 y +4 x +12 x 2 −3 x +3 Reorder the terms. 4 x +12 x +4 x −3 x −13 y +3 Combine like terms. 2 2 16 x + x −13 y +3 2
- 15. Both Skills 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
- 16. Simplifying Example 1 ( 6 x + 10) + 3( x − 4) 2
- 17. Simplifying Example Distribute. 1 ( 6 x + 10) + 3( x − 4) 2
- 18. Simplifying Example Distribute. 1 ( 6 x + 10) + 3( x − 4) 2 1 1 6 x + 10 + x( 3) − 4( 3) 2 2 3 x + 5 + 3 x −12
- 19. Simplifying Example Distribute. 1 ( 6 x + 10) + 3( x − 4) 2 1 1 6 x + 10 + x( 3) − 4( 3) 2 2 3 x + 5 + 3 x −12 Combine like terms.
- 20. Simplifying Example Distribute. 1 ( 6 x + 10) + 3( x − 4) 2 1 1 6 x + 10 + x( 3) − 4( 3) 2 2 3 x + 5 + 3 x −12 Combine like terms. 6 x −7
- 21. Evaluating Expressions Evaluate the expression 2x – 3xy +4y when x = 3 and y = -5. To find the numerical value of the expression, simply replace the variables in the expression with the appropriate number. Remember to use correct order of operations.
- 22. Example Evaluate 2x–3xy +4y when x = 3 and y = -5. Substitute in the numbers. 2(3) – 3(3)(-5) + 4(-5) Use correct order of operations. 6 + 45 – 20 51 – 20 31
- 23. Evaluating Example Evaluate x 2 − 4 xy + 3 y 2 when x = 2 and y = −1
- 24. Evaluating Example Evaluate x − 4 xy + 3 y when x = 2 and y = −1 2 2 Substitute in the numbers.
- 25. Evaluating Example Evaluate x − 4 xy + 3 y when x = 2 and y = −1 2 2 Substitute in the numbers. ( 2) 2 − 4( 2)( −1) + 3( −1) 2
- 26. Evaluating Example Evaluate x 2 − 4 xy + 3 y 2 when x = 2 and y = −1 Substitute in the numbers. ( 2) 2 − 4( 2)( −1) + 3( −1) 2 Remember correct order of operations. 4 − 4( 2)( − 1) + 3(1) 4+ + 8 3 15