SOLUTION: Please help me solve this problem. I need to find the product of (x+6)cubed. Not sure how to type the exponent 3
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Question 298081: Please help me solve this problem. I need to find the product of (x+6)cubed. Not sure how to type the exponent 3
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Use the caret mark (^ - shift-6) to indicate raising to a power. Your problem would be correctly rendered (x + 6)^3
^3\ =\ (x\ +\ 6)(x\ +\ 6)^3\ =\ (x\ +\ 3)(x^2\ +\ 12x\ +\ 36)\ =\ x^3\ +\ 18x^2\ +\ 108x\ +\ 216)
In general, ^3\ =\ a^3\ +\ 3a^2b\ +\ 3ab^2\ + b^3)
Even more in general,
^n\ =\ \left(n\cr0\right)a^nb^0\ +\ \left(n\cr1\right)a^{n-1}b^1\ +\ \left(n\cr2\right)a^{n-2}b^2\ +\ \cdots\ +\ \left(\ n\cr n-2\right)a^2b^{n-2}\ +\ \left(\ n\cr n-1\right)a^1b^{n-1}\ +\ \left(n\cr n\right)a^0b^n)
Where )
is the number of ways to choose 
things taken 
at a time and is equal to !})
John
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