Answer: " 2x⁴ − 4x³ + 10x² − 16x + 8 " .
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Step-by-step explanation:
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Given:
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Solve: 2(x−1)² (x² + 4) ;
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First, let us expand the following:
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(x−1)² = (x−1)(x−1) = x² − 1x − 1x + 1 = x² − 2x + 1 .
Now, multiply that value by "2" ;
2(x² − 2x + 1) = 2x² − 4x + 2 ;
Now, multiply this value by "(x² + 4)" ;
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(2x² − 4x + 2) (x² + 4) =
(2x² * x²) + (2x² * 4) − (4x*x²) − (4x*4) + (2*x²) + (2*4) =
2x⁴ + 8x² − 4x³ − 16x + 2x² + 8 ;
Now, combine the "like terms" :
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+ 8x² + 2x² = 10x² ; and rewrite; to get:
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2x⁴ − 4x³ + 10x² − 16x + 8 .
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