Given Expression: Barbara started with the expression 7D + 63. This expression represents a term with a coefficient of 7 multiplied by a variable D, added to the constant term 63.
Identifying the Greatest Common Factor (GCF): The first step in using the distributive property is to identify the greatest common factor (GCF) of the terms. In this expression, the terms are 7D and 63. The GCF of 7D and 63 is 7.
Dividing Each Term by the GCF: To apply the distributive property, we divide each term by the GCF. This step involves dividing both 7D and 63 by 7.
For 7D/7, the 7s cancel out, leaving just D.
For 63/7, we perform the division to find that it equals 9.
Simplifying Each Term: After dividing each term by the GCF, we simplify them. So, 7D/7 simplifies to just D, and 63/7 simplifies to 9.
Rewriting the Expression: Now that we have simplified terms, we rewrite the expression using these simplified terms. We take the simplified terms (D and 9) and put them back into the expression.
So, instead of 7D + 63, we rewrite it as 7(D + 9).
By applying the distributive property correctly, we end up with the expression 7(D + 9), where D + 9 represents a binomial term (a term with two parts) where D is multiplied by 7 and 9 is added to the result.
Barbara's error likely occurred because she misunderstood the application of the distributive property. Instead of correctly factoring out the GCF from both terms, she mistakenly factored out only the GCF from the constant term, resulting in the incorrect expression (D + 63) instead of (7D + 9).
