If (3x-1)^7=a_7x^7+a_6x^6+…+a_0, then a_7+a_6+…+a_0 equals

1977 AMC 12 Problem 10

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10.

(3x-1)^7=a_7x^7+a_6x^6+\cdots+a_0,

then

a_7+a_6+\cdots+a_0

equals

0

1

64

-64

128

A polynomial’s coefficient sum is obtained by evaluating it at a particular input

Substitute

x=1

into the given identity

Setting

x=1

makes the right side the desired coefficient sum. Thus

\begin{aligned} a_7+a_6+\cdots+a_0 &=(3\cdot1-1)^7\\ &=2^7=128. \end{aligned}

Therefore, the correct answer is E.