Question
Expand $(2 x-a)^{5}$
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Answer
$(2 x-a)^{5}$
$={ }^{5} C_{0}(2 x)^{5}(a)^{0}-{ }^{5} C_{1}(2 x)^{4}(a)^{1}+{ }^{5} C_{2}(2 x)^{3}(a)^{2}-{ }^{5} C_{3}(2 x)^{2}(a)^{3}$ $+{ }^{5} C_{4}(2 x)^{1}(a)^{4}-{ }^{5} C_{5}(2 x)^{0}(a)^{5}$
$=32 x^{5}-5\left(16 x^{4}\right)(a)+10\left(8 x^{3}\right)\left(a^{2}\right)-10\left(4 x^{2}\right)\left(a^{3}\right)+5(2 x)\left(a^{4}\right)-a^{5}$
$=32 x^{5}-80 x^{4} a+80 x^{3} a^{2}-40 x^{2} a^{3}+10 x a^{4}-a^{5}$
$={ }^{5} C_{0}(2 x)^{5}(a)^{0}-{ }^{5} C_{1}(2 x)^{4}(a)^{1}+{ }^{5} C_{2}(2 x)^{3}(a)^{2}-{ }^{5} C_{3}(2 x)^{2}(a)^{3}$ $+{ }^{5} C_{4}(2 x)^{1}(a)^{4}-{ }^{5} C_{5}(2 x)^{0}(a)^{5}$
$=32 x^{5}-5\left(16 x^{4}\right)(a)+10\left(8 x^{3}\right)\left(a^{2}\right)-10\left(4 x^{2}\right)\left(a^{3}\right)+5(2 x)\left(a^{4}\right)-a^{5}$
$=32 x^{5}-80 x^{4} a+80 x^{3} a^{2}-40 x^{2} a^{3}+10 x a^{4}-a^{5}$
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