Expand (-2x+4)^5 using the binomial theorem (Pascals triangle) Will award brainiest, (show work)

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Step-by-step explanation:

We must expand using the Binomial Theorem.

To do so, we need Pascal's Triangle. Seeing that the exponent is 5, we look at the 5 + 1 = 6th row of Pascal's Triangle. The numbers here are:

1, 5, 10, 10, 5, 1

These will be the numbers to multiply all the distinct terms in the expansion by.

Remember that when expanding this out, we always start by taking the first term (-2x here) to the nth power (here, it's 5th power) and multiplying that by the second term (4 here) to the 0th power:

(-2x)^5 * 4^0 = -32x^5 * 1 = -32x^5

Since this is our first term, we multiply it by the first Pascal number from above: 1. Then, we simply get -32x^5 as our final first term of the expansion.

We repeat this process, each time lowering the first power by 1 and increasing the second power by 2.

2nd term:

(-2x)^4 * 4^1 = 16x^4 * 4 = 64x^4

Multiply by 5:

64x^4 * 5 = 320x^4

3rd term:

(-2x)^3 * 4^2 = -8x^3 * 16 = -128x^3

Multiply by 10:

-128x^3 * 10 = -1280x^3

4th term:

(-2x)^2 * 4^3 = 4x^2 * 64 = 256x^2

Multiply by 10:

256x^2 * 10 = 2560x^2

5th term:

(-2x)^1 * 4^4 = -2x * 256 = -512x

Multiply by 5:

-512x * 5 = -2560x

6th term:

(-2x)^0 * 4^5 = 1 * 1024 = 1024

Multiply by 1:

1024 * 1 = 1024

Hence, our expansion is:

b

step-by-step explanation:

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