# 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.
The distribution property is: 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.
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 Ã— 2 = 3(2) = 3(x + 2) factor out the common factor 3 |

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