Answer
Once upon a time in the 8th century, there was a brave knight who lived in the kingdom of Scandinavia. His name was Sir Ector. One day he was walking to the market, then he ran into the king. "Ahh, just the knight I was looking for," said the king. "Hello, King Jonah," said Ector. "I need you to come to the castle. I have some essential news," said the king. Soon they had reached the castle. "I've got word that there is a terrible dragon who is terrorizing nearby kingdoms," said King Jonah. "So you want me to go kill it," said Ector. "No, I want you to take this team of knights to its lair and then kill it," said King Jonah pointing to the seven knights next to him. "Ok, I shall go first thing tomorrow," said Ector.
The correct answer is: [A]: " - 8d +<span> 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 ;
</span> 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 <u><em>NOT</em></u> among <em><u>ANY</u></em> 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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