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Simplifying Numeric Expressions Combining Like Terms Distributive Property

Discover how to simplify numeric expressions by identifying and combining like terms, and applying the distributive property. Learn to combine similar variables, ensuring they have the same exponent, and practice examples like (4x + 3x = 7x) or (2x^2 + 3x + 7x = 2x^2 + 10x). Understand the distributive property with expressions like (a(b + c)= ab + ac) and explore how to simplify operations systematically. This guide provides clear explanations and practice problems to enhance your mathematical skills.

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Simplifying Numeric Expressions Combining Like Terms Distributive Property

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  1. Simplifying Numeric ExpressionsCombining Like TermsDistributive Property Objective: Identify and combine like terms and apply the distributive property.

  2. Combine • 4 things + 3 things = 7 things • 4 apples + 3 apples = 7 apples • 4x + 3x = 7x • 4 apples + 3 oranges = 4 apples + 3 oranges You can’t combine different objects!

  3. Like Terms • Like terms must have the same variable or variables. • The variables must have the same exponent.

  4. Like Terms? Yes or No? Yes • 6y and 7y • 6y2 and 7y3 No • 3c and 3d No • 9ab and 4ab Yes • 2x2y and 3xy2 No

  5. Combine Like Terms 7x + 2y • 3x + 4x + 2y = *When combining like terms, the exponent does not change. • 3t2 + 4t2 = 7t2 • 3t2 + 4t3 = 3t2 + 4t3 (cannot be combined)

  6. Distributive Property • Allows you to multiply across a set of parenthesis • a(b + c) = a(b) + a(c) • a(b – c) = a(b) – a(c) • (b + c)a = a(b) + a(c) • (b – c)a = a(b) – a(c)

  7. Try These • 3(x + 2) = • 3(x – 2) = • -3(x + 2) = • -3(x – 2) = 3(x) + 3(2) = 3x + 6 3(x) – 3(2) = 3x – 6 -3(x) + (-3)(2) -3x – 6 = -3x + (-6) = -3(x) – (-3)(2) = -3x + 6

  8. Simplified? • All operations are completed by following the order of operations. • Grouping symbols are eliminated.

  9. Try These 3x – 12 – 10 = 3x – 22 • 3(x – 4) – 10 = • 3x + 4x2 + 7x – 2x2 = • 4x + 3(x – 5) – 2x Combine Distribute 2x2 + 3x + 7x = 2x2 + 10x Combine Combine = 4x + 3x – 15 – 2x Distribute Combine = 5x – 15

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