Answer: The simplified expression is: " 5x² + x – 7 " .
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Note:
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We are given:
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→ " (7x² + 4x – 6) – (2x² – 3x + 1) " ;
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Let us simplify this expression:
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Rewrite as:
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(7x² + 4x – 6) – 1(2x² – 3x + 1) ;
{Since there is an implied "one", since "1" ; multiplied by any value, results in the same value} ;
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Let us start with the following part of the expression:
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→ " – 1(2x² – 3x + 1) " ;
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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: " a(b – c + d) = ab – ac + ad " ;
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So:
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→ " – 1(2x² – 3x + 1) " = (-1 * 2x²) – (-1* -3x) + (-1 * 1) ;
= -2x² – 3x + (-1) ;
= -2x² – 3x – 1 ;
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Now, bring down the: " 7x² + 4x – 6 " ; and add the " – 2x² – 3x – 1 " ;
as follows:
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→ " 7x² + 4x – 6 – 2x² – 3x – 1 " ;
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→ Combine the "like terms" :
+ 7x² – 2x² = + 5x² ;
+ 4x – 3x = + 1x = + x ;
– 6 – 1 = – 7 ;
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And we can rewrite the simplified expression as:
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→ " 5x² + x – 7 " .
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