The correct answer is: [A]: " - 8d + 3 " .
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Explanation:
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Note the "distributive property" of multiplication:
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a(b + c) = ab + ac ;
a(b − c) = ab − ac .
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We are given the expression:
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" - (8d − 3w) " ; and are asked for the simplified expression;
Consider this as:
" -1 (8d − 3w) " ;
The "1" (in this case, "-1" ; since the "negative" sign is already present; is "implied" ; since any value, multiplied by "1", results in that very same value.
So, using the "distributive property of multiplication" ; as explained above ;
→ " -1 (8d − 3w) = (-1 * 8d) − (-1 * 3w) ;
= - 8d − (-3w) ;
= - 8d + 3w ; → {since "subtracting a negative" is the
same thing as "adding a positive"};
This answer corresponds to: "Answer choice: [A]: " - 8d + 3w " .
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An additional note of interest:
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Another simplified form of the expression would be: " 3w − 8d " ;
HOWEVER, this is NOT among ANY of the answer choices given.
Note: Consider our answer choice: " [A]: " - 8d + 3w " ;
Note: " - 8d + 3w = 3w + (- 8d) = " 3w − 8d " ;
→ {since "adding a negative" is the same as "subtracting a positive" .}.
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So; note that:
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→ " - (x − y) = (y − x) " .
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