Math with Mr. Jay: Introduction to Simplifying Algebraic Expressions Using the Distributive Property

Overview of the Distributive Property

• The distributive property helps remove parentheses within algebraic expressions.
• It's useful when there are no like terms within parentheses to combine.
• When something is next to parentheses, it indicates multiplication.
• Distributive property distributes the term outside the parentheses to each term inside.
• It works with addition or subtraction inside the parentheses.

General Overview

• Illustrated with example: a(b + c) = ab + ac.
• The property maintains the value of the expression.

Examples

Example 1: Numerical Expression

• Expression: 2(5 + 3)
• Solving with Order of Operations:
  • Calculate inside the parentheses first: 5 + 3 = 8.
  • Then, multiply: 2 * 8 = 16.
• Solving with Distributive Property:
  • Distribute 2 to 5 and 3: (2 * 5) + (2 * 3)
  • Calculate: 10 + 6 = 16.
• Conclusion: Both methods yield 16, showing the property doesn't change expression value.*

Example 2: Algebraic Expression

• Expression: 8(2m + 6)
• Can't combine terms inside parentheses.
• Apply Distributive Property:
  • Distribute 8 to 2m and 6: (8 * 2m) + (8 * 6)
  • Calculate: 16m + 48.
• Result: Simplified expression is 16m + 48 with no like terms to combine.

Example 3: Involving Subtraction

• Expression: 7(a - 9)
• Apply Distributive Property:
  • Distribute 7 to a and -9: (7 * a) - (7 * 9)
  • Calculate: 7a - 63.
• Alternative Method:
  • Treat subtraction as negative 9: 7(-9)
  • Calculate similarly for same result.
• Result: Simplified expression is 7a - 63.

Example 4: Negative Coefficients

• Expression: 10(-5x - 4y)
• Apply Distributive Property:
  • Distribute 10 to -5x and -4y: (10 * -5x) - (10 * 4y)
  • Calculate: -50x - 40y.
• Alternative Method:
  • Treat subtraction as negative: 10(-4y)
  • Calculate similarly for same result.
• Result: Simplified expression is -50x - 40y.

Conclusion

• Introduction to using the distributive property with numerical and algebraic expressions.
• Emphasized value consistency and alternative thinking methods.
• For further examples, refer to Part 2 of the series.

Thank you for watching and learning the basics of the distributive property with Mr. Jay. For more practice, check further lessons.