Question

How do you expand `(d + 5)^7` using Pascal’s Triangle?

Answer 1

You take the seventh row of Pascal's triangle (remember, the 1 at the top counts as row 0)

Explanation:

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In case of `(a+b)^7` the expansion goes like:

`1*a^7*b^0+7*a^6*b^1+21*a^5*b^2..... 7*a^1*b^6+1*a^0*b^7`

The exponents of the first run down from `7->0` and the ones of the other go up from `0->7`. They add up to `7` all the time.

In your case this would be:

`1*d^7*5^0+7*d^6*5^1+21*d^5*5^2+35*d^4*5^3...` and so on
untill `1*d^0*5^7`

`=d^7+35d^6+525d^5...` etc.