Question
Evaluate: $(4x^2 - 4x + 1)(2x^3 - 3x^2 + 2)$
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Answer
$(4x^2 - 4x + 1)(2x^3 - 3x^2 + 2)$
$= 4x^2 (2x^3 - 3x^2 + 2) - 4x (2x^3 - 3x^2 + 2) + 1 (2x^3 - 3x^2 + 2)$
$= 8x^5 - 12x^4 + 8x^2 - 8x^4 + 12x^3 - 8x + 2x^3 - 3x^2 + 2$
$= 8x^5 - 12x^4 - 8x^4 + 12x^3 + 2x^3 + 8x^2 - 3x^2 - 8x + 2$
$= 8x^5 - 20x^4 + 14x^3 + 5x^2 - 8x + 2$
$= 4x^2 (2x^3 - 3x^2 + 2) - 4x (2x^3 - 3x^2 + 2) + 1 (2x^3 - 3x^2 + 2)$
$= 8x^5 - 12x^4 + 8x^2 - 8x^4 + 12x^3 - 8x + 2x^3 - 3x^2 + 2$
$= 8x^5 - 12x^4 - 8x^4 + 12x^3 + 2x^3 + 8x^2 - 3x^2 - 8x + 2$
$= 8x^5 - 20x^4 + 14x^3 + 5x^2 - 8x + 2$
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