Question

How do I use Pascal's triangle to expand a binomial?

Answer 1

Rows of Pascal's triangle provide the coefficients to expand `(a+b)^n` as follows...

Explanation:

To expand `(a+b)^n` look at the row of Pascal's triangle that begins `1, n`. This provides the coefficients.

For example, `(a+b)^4 = a^4+4a^3b+6a^2b^2+4ab^3+b^4` from the row `1, 4, 6, 4, 1`

How about `(2x-5)^4` ?

Let `a = 2x` and `b = -5`.

Then:

`(2x-5)^4 = (a+b)^4 = a^4+4a^3b+6a^2b^2+4ab^3+b^4`

`=(2x)^4+4(2x)^3(-5)+6(2x)^2(-5)^2+4(2x)(-5)^3+(-5)^4`

`=16x^4+4(8x^3)(-5)+6(4x^2)(25)+4(2x)(-125)+(625)`

`=16x^4-160x^3+600x^2-1000x+625`