LESSON - Simplifying Algebraic Expressions

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.

Simplifying Algebraic Expressions

Algebraic Expressions

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

ASSESSMENT:
SIMPLIFY the following ALGEBRAIC EXPRESSIONS

Multiple Choice

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

• 13x

• 11x

• 12x

• 10x

Multiple Choice

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

• 10x

• 8x-6

• 10x-12

• 8x-12

Multiple Choice

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

• 0

• -6y

• -4y

• -5y

Multiple Choice

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

• 5x + 7

• 9x + 19

• 4x + 17

• 4x + 23

Multiple Choice

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

• -2x +8

• -2x - 6

• 2x + 6

• -2x + 6

Multiple Choice

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

• 6y - 12

• 6y + 12

• 8y - 6

• 8y + 6

Multiple Choice

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

• 8x

• 8y

• 8x + 2y

• 8x - 2y

Multiple Choice

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

• 7a - 7b

• 7a - 3b

• a - 3b

• 7a - 5b

Multiple Choice

Simplify: 2(3x + 5) - x

• 5x -10

• 6x + 8

• 5x + 10

• 6x + 10

Multiple Choice

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

• 2y - 3

• 2y + 3

• 6y - 3

• 6y + 3

Multiple Choice

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

• 6x

• 8x

• 5x

• 10x

Multiple Choice

Simplify: 3(2a - 5) + 4(a + 2)

• 10a - 7

• 10a + 7

• 6a - 7

• 6a + 7

Multiple Choice

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

• 8x - y

• 8x + 3y

• 8x - 2y

• 4x + y

Multiple Choice

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

• 6x + 13

• -2x +11

• 13 - 6x

• -6x - 13

Multiple Choice

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

• 11y - 4

• 13y - 4

• 11y + 4

• 13y + 4

Multiple Choice

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

• 7a + 3b

• 7a - 3b

• a + 3b

• 7a + 5b

Multiple Choice

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

• -6x - 12

• 12 - 6x

• -12

• 0

Multiple Choice

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

• -x + 6y

• B. -x + 2y

• x + 6y

• -x + 4y

Multiple Choice

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

• - 11b

• 6a - 11b

• -6a + 11b D

• 6a + 11b

Multiple Choice

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

• 23x - 8

• 23x + 8

• 13x + 8

• 13x - 8

Multiple Choice

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

• 7y - 6

• 7y + 6

• 4y - 6

• 4y + 6

Multiple Choice

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

• 8x - 3y

• 8x + y

• 2x - 3y

• 2x + y

Multiple Choice

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

• 8y + 2

• 2y + 5

• 8y - 2

• 2y - 2

Multiple Choice

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

• 10x + 6

• 14x - 6

• 16x - 6

• 10x - 6

Multiple Choice

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

• -9a + 22

• -9a-22

• 15a + 26

• 15a - 26

Multiple Choice

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

• 2x + y

• 8x + y

• 2x - 3y

• 8x - 3y

Multiple Choice

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

• -x + 6y

• -x + 2y

• x + 6y

• -x + 4y

Multiple Choice

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

• 7a - 7b

• 7a - 3b

• a - 3b

• 7a - 5b

Multiple Choice

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

• 2x + 10

• 2x +14

• 10 - 2x

• 13x - 8

Multiple Choice

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

• 8x - 3y

• 8x + y

• 2x - 3y

• 2x + y

Multiple Choice

Combine like terms: $$15x^2+13y^2-12x^2-9y^2+5x^3$$

• 
  $$3x^2+4y^2+5x^3$$

• $$8x^5+4y^2$$

• $$12x^2y^2$$

• $$3x^2-4y^2+5x^3$$

Multiple Choice

Combine like terms: $$4x^2-6x-x^2+13x+13y-7$$

• 
  $$3x^2+13y-7$$

• $$3x^2+7x+13y-7$$

• $$3x^2+7x+5y$$

• $$3x^2+20xy-7$$

Multiple Choice

Combine like terms: $$9\left(7x+4y\right)-8\left(3x+2y\right)$$

• 
  $$63x+36y$$

• $$29x+36y$$

• $$39x-16y$$

• $$39x+20y$$

Draw

Draw your solution on the canvas. Simplify: $$4x^2-6x-x^2+13x+13y-7$$