Learn on PengiBig Ideas Math, Advanced 1Chapter 3: Algebraic Expressions and Properties

Lesson 4: The Distributive Property

In this Grade 6 lesson from Big Ideas Math Advanced 1, students learn the Distributive Property and how it applies to both arithmetic and algebra, including the rules a(b + c) = ab + ac and a(b − c) = ab − ac. Students practice using the property as a mental math strategy for multiplying multi-digit numbers and mixed numbers, then extend the skill to simplifying algebraic expressions such as 4(n + 5) and 12(2y − 3). The lesson aligns with Common Core standards 6.NS.4, 6.EE.3, and 6.EE.4 within the Algebraic Expressions and Properties chapter.

Section 1

Distributive Property with Variables

Property

When multiplying a number by a sum or difference in parentheses, you can distribute the multiplication to each term inside the parentheses.

For algebraic expressions:

a(b+c)=ab+aca(b + c) = ab + ac
a(bc)=abaca(b - c) = ab - ac

Section 2

Combining Like Terms

Property

Like terms are terms that involve the same variable raised to the same exponent. Constants are also like terms.
The importance of distinguishing like terms is that they can be combined to make the expression easier to read and compute, a process called simplifying.

Examples

  • To simplify 7x+5+3x7x + 5 + 3x, combine the like terms 7x7x and 3x3x to get 10x10x. The simplified expression is 10x+510x + 5.
  • To simplify 9a+4b+2ab9a + 4b + 2a - b, combine the aa terms (9a+2a=11a9a+2a=11a) and the bb terms (4bb=3b4b-b=3b). The result is 11a+3b11a + 3b.
  • To simplify 12+5y8+2y12 + 5y - 8 + 2y, combine the constants (128=412-8=4) and the yy terms (5y+2y=7y5y+2y=7y). The result is 7y+47y + 4.

Explanation

Combining like terms is like organizing your toys. You can put all the toy cars together and all the building blocks together, but you can't mix them. In math, you add or subtract terms with the same variable part.

Book overview

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Chapter 3: Algebraic Expressions and Properties

  1. Lesson 1

    Lesson 1: Algebraic Expressions

  2. Lesson 2

    Lesson 2: Writing Expressions

  3. Lesson 3

    Lesson 3: Properties of Addition and Multiplication

  4. Lesson 4Current

    Lesson 4: The Distributive Property

Lesson overview

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Section 1

Distributive Property with Variables

Property

When multiplying a number by a sum or difference in parentheses, you can distribute the multiplication to each term inside the parentheses.

For algebraic expressions:

a(b+c)=ab+aca(b + c) = ab + ac
a(bc)=abaca(b - c) = ab - ac

Section 2

Combining Like Terms

Property

Like terms are terms that involve the same variable raised to the same exponent. Constants are also like terms.
The importance of distinguishing like terms is that they can be combined to make the expression easier to read and compute, a process called simplifying.

Examples

  • To simplify 7x+5+3x7x + 5 + 3x, combine the like terms 7x7x and 3x3x to get 10x10x. The simplified expression is 10x+510x + 5.
  • To simplify 9a+4b+2ab9a + 4b + 2a - b, combine the aa terms (9a+2a=11a9a+2a=11a) and the bb terms (4bb=3b4b-b=3b). The result is 11a+3b11a + 3b.
  • To simplify 12+5y8+2y12 + 5y - 8 + 2y, combine the constants (128=412-8=4) and the yy terms (5y+2y=7y5y+2y=7y). The result is 7y+47y + 4.

Explanation

Combining like terms is like organizing your toys. You can put all the toy cars together and all the building blocks together, but you can't mix them. In math, you add or subtract terms with the same variable part.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 3: Algebraic Expressions and Properties

  1. Lesson 1

    Lesson 1: Algebraic Expressions

  2. Lesson 2

    Lesson 2: Writing Expressions

  3. Lesson 3

    Lesson 3: Properties of Addition and Multiplication

  4. Lesson 4Current

    Lesson 4: The Distributive Property