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

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Answer 1 · 2018-04-22T03:33:18

$x^5 - 15 x^4 + 90 x^3 - 270x^2 +405 x - 243$

We need the row that starts with $1\ 5$ .

       1
    1 2 1
 1  3  3  1
1  4  6   4  1

1 5 10 10 5 1

$(x-3)^5$

$= x^5 + 5 x^4 (-3)^1 + 10 x^3 (-3)^2 + 10 x^2 (-3)^3 + 5 x (-3^4 )+ 3^5$

$= x^5 - 15 x^4 + 90 x^3 - 270x^2 +405 x - 243$

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