AS maths help? Binomial expansion?

I you find it difficult to remember the formula for the Binomial Theorem, so instead if you notice that the powers on each term in the expansion always added up to whatever n is, and that the terms counted up from zero to n.

Returning to your question of (5 - 2x)^5 or

(-1)^5 * [(2x - 5)^5], the powers on every term of the expansion will add up to 5, and the powers on the terms will increment by counting up from zero to 5:

[(2x – 5)^5] = 5C0 (2x)^(5–0) * (–5)^0 + 5C1 (2x)^(5–1) * (–5)^1 + 5C2 (2x)^(5–2) * (–5)^2

+ 5C3 (2x)^(5 - 3) * (–5)^3 + 5C4 (2x)^(5 - 4) * (–5)^4 + 5C5 (2x)^(5–5) * (–5)^5

Note how the counter number counts up from zero to 5, with the factors on the ends of each term having the counter number, and the factor in the middle having the counter number subtracted from 5. This pattern is all you really need to know about the Binomial Theorem; this pattern is how it works.

so 5C2 (2x)^(5–2) * (–5)^2 will be the term containing x^3

so coefficient of x^3 in the expansion would be

= (-1)^5 [5C2 * 2^3 * (-5)^2] ; which is

= - [ 10 * 8 * 25]

= - 2000 will be your answer

and expansion would be

(5 - 2x)^5 = -32x^5 + 400x^4 - 2000x^3 + 5000x^2 - 6250x + 3125

Hope this helped

Vick

There are two main ways of stating the Binomial expansion.

I will use the "old-fashioned" way:

(1 + x)^n = 1 + nx + [n(n - 1)x^2/2!] +[n(n - 1)(n -2)x^3/3!] +....

(5 - 2x)^5...... Take a factor of 5 out of the brackets

= 5^5(1 - 2x/5)^5

So in the general binomial expansion I quoted above replace x by (-2x/5) and n by 5

Then multiply each term by 5^5.