How do I use the binomial theorem to expand ${(d - 4 b)}^{3}$ $(d-4b)^3$ ?

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How do I use the binomial theorem to expand ${(d - 4 b)}^{3}$ $(d-4b)^3$ ?

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Answer 1 · 2018-03-15T09:48:51

$d^{3} - 12 b d^{2} + 48 b^{2} d - 64 b^{3}$ $d^3-12bd^2+48b^2d-64b^3$

Refer to the explanation.

Explanation:

${(d - 4 b)}^{3}$ $(d-4b)^3$

Using binomial theorem,

$C (3, 0) \cdot d^{3} \cdot {(4 b)}^{0} - C (3, 1) \cdot d^{3 - 1} \cdot {(4 b)}^{1}) + C (3, 2) \cdot d^{3 - 2} \cdot {(4 b)}^{2} - C (3, 3) \cdot d^{3 - 3} \cdot {(4 b)}^{3}$ $C(3,0) * d^3*(4b)^0 - C(3,1) * d^(3-1) * (4b)^1)+C(3,2) * d^(3-2) * (4b)^2 - C(3,3)* d^(3-3) * (4b)^3$
$d^{3} - 3 \cdot d^{2} \cdot 4 b + 3 \cdot d \cdot 16 b^{2} - 64 b^{3}$ $d^3-3*d^2*4b +3*d*16b^2-64b^3$

$d^{3} - 12 b d^{2} + 48 b^{2} d - 64 b^{3}$ $d^3-12bd^2+48b^2d-64b^3$

That's it. Hope it helps :)

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How do I use the binomial theorem to expand ${(d - 4 b)}^{3}$ $(d-4b)^3$ ?

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