Simplifying Numeric Expressions Combining Like Terms Distributive Property

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

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!

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

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

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)

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)

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

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

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

Simplifying Numeric Expressions Combining Like Terms Distributive Property