Expand the following binomial by using Pascal's Triangle.
$$( 2 x - 4 ) ^ { 5 }$$
A) $32 x ^ { 5 } - 1024$
B) $- 1024 x ^ { 5 } + 1280 x ^ { 3 } + 32$
C) $32 x ^ { 5 } - 320 x ^ { 4 } + 1280 x ^ { 3 } - 2560 x ^ { 2 } + 2560 x - 1024$
D) $32 x ^ { 5 } + 2560 x ^ { 4 } - 2560 x ^ { 3 } + 1280 x ^ { 2 } - 320 x - 1024$
E) $ 32 x ^ { 5 } - 64 x ^ { 4 } + 128 x ^ { 3 } - 256 x ^ { 2 } + 512 x - 1024$

Question

Quizplus · Accepted Answer

We can use Pascal's Triangle to expand the binomial as follows:

$$(2x-4)^5 = \binom{5}{0}(2x)^5(-4)^0+\binom{5}{1}(2x)^4(-4)^1+\binom{5}{2}(2x)^3(-4)^2+\binom{5}{3}(2x)^2(-4)^3+\binom{5}{4}(2x)^1(-4)^4+\binom{5}{5}(2x)^0(-4)^5$$

Simplifying this expression gives:

$$32x^5-320x^4+1280x^3-2560x^2+2560x-1024$$

Therefore, the best choice is C.

Expand the Following Binomial by Using Pascal's Triangle (2x−4)5( 2 x - 4 ) ^ { 5 }(2x−4)5

Expand the Following Binomial by Using Pascal's Triangle $( 2 x - 4 ) ^ { 5 }$