Expression Simplification

AHA TRIVA ABOUT ALGEBRA

The word "algebra" comes from the Arabic "al-jabr," used by the mathematician al-Khwarizmi in the 9th century. "Al-jabr" refers to the process of restoring or balancing equations. This laid the foundation for algebra as a branch of mathematics dealing with symbols and variables to solve equations and study relationships between quantities.

LESSON PROPER

Algebraic expressions often appear complex at first, but by applying some fundamental rules, we can simplify them and make them more manageable. The key is to understand and use the basic properties of algebra to combine like terms and reduce the expression to its simplest form.

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LIKE TERMS

​Like terms are terms that have the same variable(s) raised to the same power. For example, 3x and 5x are like terms because they both have the variable x raised to the power of 1.

To simplify, combine like terms by adding or subtracting their coefficients.

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Simplify: 2x + 4y - 3x - 2y

• Combine like terms:

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

  = -x + 2y

EXAMPLE

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DISTRIBUTIVE PROPERTY

• The distributive property allows us to multiply a term outside the parentheses by each term inside the parentheses.

• a(b + c) = ab + ac

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Simplify: 3(2x + 5)

• Distribute 3 to each term inside the parentheses:

• 3 (2x )+ 3 (5 )= 6x + 15

EXAMPLE

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COMBINING LIKE TERMS WITH DISTRIBUTION

• Use the distributive property when you need to distribute a factor to each term inside parentheses before combining like terms.

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Simplify: 2(3x - 4) - x

• Distribute 2 to each term inside the first set of parentheses:

  2 (3x )- 2 (4) - x = 6x - 8 - x

• Combine like terms:

  (6x - x) - 8 = 5x - 8

EXAMPLE

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REMOVING
PARENTHESIS

• If an expression is entirely in parentheses with no addition or subtraction outside, you can remove the parentheses.

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Simplify: 2(3x + 7) - 4(2x - 5)

• Distribute and combine like terms:

  6x + 14 - 8x + 20

• Combine like terms:

  (6x - 8x) + (14 + 20)

  = -2x + 34

EXAMPLE

PRACTICE PROBLEM

​Simplify the following expressions:

1. 4x + 2y - 3x + 5y

2. 2(5x - 3)

3. 3(2x + 4) - 2(3x - 1)

ASSESSMENT:
ALGEBRAIC EXPRESSION

Multiple Choice

1. 1. Simplify: 3x + 5x - 2x + 7x

• 13x

• 11x

• 12x

• 10X

Multiple Choice

2. 2.What is the simplified form of 4(2x - 3) + 2x?

• 10X

• 8X-6

• 10X-6

• 8X-12

Multiple Choice

3.Combine like terms: 2y + 3y - 5y

• A. 0

• B. -6y

• C. -4y

• D. -5y

Multiple Choice

4. 4.Simplify: 5(2x + 4) - 3(2x - 1)

• A. 5x + 7

• B. 9x + 19

• C. 4x + 11

• D. 5x + 11

Multiple Choice

5.What is the result of 2(x + 3) - 4x?

• A. 2x - 6

• B. -2x - 6

• C. 2x + 6

• D. -2x + 6

Multiple Choice

6.What is the result of 4(2y - 3) - 2y?

• A. 6y - 12

• B. 6y + 12

• C. 8y - 6

• D. 8y + 6

Multiple Choice

7Combine like terms: 3x - 2y + 5x + 2y

• A. 8x

• B. 8y

• C. 8x + 2y

• D. 8x - 2y

Multiple Choice

8.Combine like terms: 3a - 2b + 4a - 5b

• A. 7a - 7b

• B. 7a - 3b

• C. a - 3b

• D. 7a - 5b

Multiple Choice

9.Simplify: 2(3x + 5) - x

• A. 5x + 10

• B. 6x + 8

• C. 5x + 8

• D. 6x + 10

Multiple Choice

10.What is the simplified form of 4y - (2y + 3)?

• A. 2y - 3

• B. 2y + 3

• C. 6y - 3

• D. 6y + 3

Multiple Choice

11. 11.Combine like terms: 7x - 3x + 2x

• A. 6x

• B. 8x

• C. 5x

• D. 10x

Multiple Choice

11. 12.Simplify: 3(2a - 5) + 4(a + 2)

• 11. A. 10a - 7

• 11. B. 10a + 7

• 11. C. 6a - 7

• 11. D. 6a + 7

Multiple Choice

13.Combine like terms: 3x - 2y + 5x + y

• A. 8x - y

• B. 8x + 3y

• C. 8x - 2y

• D. 4x + y

Multiple Choice

14.What is the result of 2(4x + 3) - 5(2x - 1)?

• A. 6x + 13

• B. 6x - 13 C

• . 13 - 6x

• D. -6x - 13

Multiple Choice

15.Simplify: 2(5y - 2) + 3y

• A. 11y - 4

• B. 13y - 4

• C. 11y + 4

• D. 13y + 4

Multiple Choice

16.Combine like terms: 4a - 2b + 3a + 5b

• A. 7a + 3b

• B. 7a - 3b

• C. a + 3b

• D. 7a + 5b

Multiple Choice

17.What is the simplified form of 6(2x - 1) - 3(4x + 2)?

• A. -6x - 12

• B. 12 - 6x

• C. -6x + 12

• D. 12 + 6x

Multiple Choice

18.Simplify: 2x + 4y - 3x + 2y

• A. -x + 6y

• B. -x + 2y

• C. x + 6y

• D. -x + 4y

Multiple Choice

19.Combine like terms: 3(2a - b) - 2(3a + 4b)

• A. -6a - 11b

• B. 6a - 11b

• C. -6a + 11b D

• . 6a + 11b

Multiple Choice

20.What is the result of 5(3x - 2) + 2(4x + 1)?

• A. 23x - 8

• B. 23x + 8

• C. 13x + 8

• D. 13x - 8

Multiple Choice

21.Simplify: 2(2y - 3) + 3y

• A. 7y - 6

• B. 7y + 6

• C. 4y - 6

• D. 4y + 6

Multiple Choice

22.Combine like terms: 5x - 2y + 3x - y

• A. 8x - 3y

• B. 8x + y C

• . 2x - 3y

• D. 2x + y

Multiple Choice

23. 23.What is the simplified form of 5y - (3y + 2)?

• A.8y + 2

• 23. B. 2y + 5

• 23. C. 8y - 2

• 23. D. 2y - 5

Multiple Choice

24.Simplify: 4(3x - 2) + 2(2x + 1)

• A. 10x + 6

• B. 14x - 6

• C. 14x + 6

• D. 10x - 6

Multiple Choice

25.What is the result of 3(2a + 4) - 5(3a - 2)?

• A. -15a + 26

• B. -15a - 26

• C. 15a + 26

• D. 15a - 26

Multiple Choice

26.Combine like terms: 5x - 2y + 3x - y

• A. 2x + y

• B. 8x + y

• C. 2x - 3y

• D. 8x - 3y

Multiple Choice

27.Simplify: 2x + 4y - 3x + 2y

• A. -x + 6y

• B. -x + 2y

• C. x + 6y

• D. -x + 4y

Multiple Choice

28.Combine like terms: 3a - 2b + 4a - 5b

• A. 7a - 7b

• B. 7a - 3b

• C. a - 3b

• D. 7a - 5b

Multiple Choice

29.What is the simplified form of 4(2x + 3) - 2(3x - 1)?

• A. 2x + 10

• B. 2x - 10

• C. 10 - 2x

• D. 13x - 8

Multiple Choice

30.Combine like terms: 5x - 2y + 3x - y

• A. 8x - 3y

• B. 8x + y

• C. 2x - 3y D. 2x + y

• D. 2x + y