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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