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Barbara used the distributive property to write an expression that is equivalent to [tex]$7d + 63$[/tex]. Her work is shown below.

The greatest common factor is 7, so [tex]$7d + 63 = 7(d + 63)$[/tex].

What was Barbara's error?

A. Barbara wrote [tex][tex]$(\alpha^2 + 63)$[/tex][/tex] instead of [tex]$(63d)$[/tex].
B. Barbara wrote [tex]$(d + 63)$[/tex] instead of [tex][tex]$(d + 9)$[/tex][/tex].
C. Barbara wrote [tex]$(d + 63)$[/tex] instead of [tex]$(d + 56)$[/tex].
D. Barbara wrote [tex][tex]$(d + 63)$[/tex][/tex] instead of [tex]$(10d)$[/tex].

Sagot :

GinnyAnsweridn
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].
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