Expand `(3 - x)^5`

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tiburtius | High School Teacher | (Level 2) Educator

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You need to use the following formula

`(a+b)^n=sum_(k=0)^(n)((n),(k))a^(n-k)b^k`

In your case `a=3,` `b=-x` and `n=5`

`(3-x)^5=((5),(0))3^5x^0-((5),(1))3^4x+((5),(2))3^3x^2-((5),(3))3^2x^3+`

`((5),(4))3x^4-((5),(5))3^0x^5=`

`1cdot3^5-5cdot3^4x+10cdot3^3x^2-10cdot3^2x^3+5cdot3x^4-1cdotx^5=`

`243-405x+270x^2-90x^3+15x^4-x^5` 

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