$$f ( x ) = 4 x ^ { 3 } - 2 x ^ { 2 } + 4 x + 1$$
$12x^{2}-4x+4$
$$3\times 4x^{3-1}+2\left(-2\right)x^{2-1}+4x^{1-1}$$
$$12x^{3-1}+2\left(-2\right)x^{2-1}+4x^{1-1}$$
$$12x^{2}+2\left(-2\right)x^{2-1}+4x^{1-1}$$
$$12x^{2}-4x^{2-1}+4x^{1-1}$$
$$12x^{2}-4x^{1}+4x^{1-1}$$
$$12x^{2}-4x^{1}+4x^{0}$$
$$12x^{2}-4x+4x^{0}$$
$$12x^{2}-4x+4\times 1$$
$$12x^{2}-4x+4$$
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$4x^{3}-2x^{2}+4x+1$
