For example, how do you expand (2x + 6 )?

How do you expand linear expressions that involve multiplication, addition, and subtraction with fractions? For example, how do you expand (2x + 6)?

In this lesson you will learn how to expand linear expressions with rational coefficients by using an area model and the distributive property.

Vocabulary: Linear expression Rational coefficient Combine like terms + 2 = v v + 3 + v - 1

Properties of the Real Numbers: Commutative: 11 + 4 = 4 + 11 Associative: (4 + 3) + 9 = 4 + (3 + 9) Distributive: 5(6 + 2) = 5(6) + 5(2)

Failing to distribute negative numbers completely: -9(4 + 3) = -9(4) + 9(3) -

Distributing multiplication over multiplication: 3(5 2) = 3(5) 3(2) - 3(10) 15 6 - = 90 30

How do we expand (2x + 6)? 2x + 6 X + 3 X + 3 (2x + 6) = x + 3

Using the distributive property to expand (2x + 6): 2x + 6 + (6) = (2x) = x + 3 (2x + 6)

Expand and combine like terms: (5n+ 7) - 2( n- 1) = (5n) + (7) + (-2)( n) + (-2)(-1) + 2 = n + (- n) + = n +

In this lesson you have learned how to expand linear expressions with rational coefficients by using an area model and the distributive property.

Simplify: ( w + 10) - 3(w -)

Use a diagram to show why • (6y + 15) = 2y + 5.

Subtract one-half of a group of 8u + 3 from one-third of a group of 13u - 7.

Write at least two different linear expressions, using fractions, that expand and simplify to a value of 10x + 8.

1. Simplify: (9y-15) + (4y + 5) 2. Simplify: (6 - x) - 4(x - )

For example, how do you expand (2x + 6 )?