 # Use of the Distributive Property in Algebra - Grade 6

Grade 6 examples and questions on how to use the distributive property in algebra with detailed solutions and explanations are presented.

Use the Distribution Property to Expand Algebraic Expressions

a, b and c being real numbers, The distribution property is given by:

a(b + c) = (a)(b) + (a)(c) = a b + a c

To understand the distributive property, let us evaluate the expression 2(3 + 4) using two ways.

1) Use of the order of operations:

2(3 + 4)

= 2(7) group what is inside the parentheses

= 14 multiply to simplify

2) Use of the distribution property

2(3 + 4)

= (2)(3) + (2)(4) distribute the 2 over the two terms inside the parentheses.

= 6 + 8 simplify

= 14 simplify

Both methods give the same answer. But if you have to simplify or expand an expression with a variable such as

2( x + 6)

x + 6 cannot be simplified because x is a variable. Hence the use of the distribution property.

2( x + 6)

= (2)(x) + (2)(6)

= 2x + 12

Only the distribution can be used to expand 2(x + 6) because of the variable x.

Use the Distribution Property to Factor Alebraic Expressions

The distribution propery can in general be written as

a( b + c) = a b + a c

The same property can be used from right to left to factor (write as a product) expressions such as a b + a c

a b + a c = a(b + c)

Example: Factor (write as a product) the expression 3 x + 6

3 x + 6 Given

= 3 x + 3 (2) write 6 as 3 × 2 = 3(2)

= 3(x + 2) factor out the common factor 3

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