The answer is: Yes; "{-2x² + 5x}" is equivalent to "{5x − 2(x² + 6) + 12}" .
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Explanation:
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The question asks:
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"Is {-2x² + 5x} equivalent to {5x − 2(x² + 6) + 12} ?"
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First, we need to simplify the "second expression" ; then rewrite the "second expression; then rewrite the question;
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The second expression: {5x - 2(x² + 6) + 12} ;
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Let us simplify and rewrite.
First, let us expand the: -2(x² + 6) ;
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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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As such: -2(x² + 6) = -2*x² + (-2)*6 = -2x² + (-12) = -2x² − 12 ;
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So we rewrite: "{5x − 2(x² + 6) + 12} " ; as:
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{5x − 2x² − 12 + 12} = 5x − 2x²
= 5x + (-2x²) = -2x² + 5x; (rewrite with highest degree polynomial first);
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So now, we can rewrite the ORIGINAL question:
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"Is {-2x² + 5x} equivalent to {-2x² + 5x} ?"
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The answer is: Yes! These values are equal; and as such, are equivalent.
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So, the original question is:
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"Is {-2x² + 5x} equivalent to {5x − 2(x² + 6) + 12} ?
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The answer is: Yes; "{-2x² + 5x}" is equivalent to "{5x − 2(x² + 6) + 12}" .
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