The correct answer is: [A]: " 2x³ + 7x² + 12x − 8 " .
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Explanation:
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Given:
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" (x² + 4x + 8) (2x − 1) " ; Find the product:
↔ " (2x − 1) (x² + 4x + 8) " ;
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Note: " (a + b) (c + d + e) = ab + ad + ae + bc + bd + ae " .
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→ " (2x − 1) (x² + 4x + 8) =
(2x * x²) + (2x * 4x) + (2x *8) + (-1 * x²) + (-1 * 4x) + (-1 * 8) ;
= 2x³ + 8x² + 16x + (-1x²) + (-4x) + (-8) ;
= 2x³ + 8x² + 16x − x² − 4x − 8) ;
→ Combine the "like terms" :
+ 8x² − x² = + 7x² ;
+ 16x − 4x = + 12x ;
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And rewrite the expression:
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→ " 2x³ + 7x² + 12x − 8 " ;
→ which is: Answer choice: [A]: " 2x³ + 7x² + 12x − 8 " .
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