Let's analyze the expression and the steps Barbara took to apply the distributive property.
Given expression:
[tex]\[ 7d + 63 \][/tex]
To factor out the greatest common factor, we first identify the greatest common factor (GCF) of the terms in the expression, which are 7 and 63. The greatest common factor here is 7.
We can rewrite the expression by factoring out the 7:
[tex]\[ 7d + 63 = 7(d + 9) \][/tex]
Barbara’s work is shown as:
[tex]\[ 7d + 63 = 7(d + 63) \][/tex]
Barbara’s error lies in the part where she rewrites the expression inside the parentheses. Instead of simplifying [tex]\(7 \times 9\)[/tex] to write:
[tex]\[ 7(d + 9) \][/tex]
She incorrectly wrote:
[tex]\[ 7(d + 63) \][/tex]
Therefore, Barbara wrote [tex]\((d + 63)\)[/tex] instead of [tex]\((d + 9)\)[/tex].
So, Barbara's error was: Barbara wrote [tex]$(d+63)$[/tex] instead of [tex]$(d+9)$[/tex].
