Question

How do you use pascals triangle to expand `(2x-3)^5`?

Answer 1

`32x^5-240x^4+720x^3-1080x^2+810x-243`

Explanation:

you must consider the Pascal(or Tartaglia) triangle until level 5:

                                          1
                                      1        1
                                 1        2        1
                            1         3       3       1
                       1         4        6       4       1
                1           5       10       10     5        1

then you expand the terms calculating :

`color(red)1(2x)^5+color(red)5(2x)^4(-3)+color(red)10(2x)^3(-3)^2+color(red)10(2x)^2(-3)^3+color(red)5(2x)(-3)^4+color(red)1(-3)^5`

That is

`32x^5-240x^4+720x^3-1080x^2+810x-243`