Question

Expand the binomial (y+1)^8

Answer 1

Using Pascal's triangle, we can determine the coefficients and degree of each term.

The coefficients for the formula will be: 1, 8, 28, 56, 70, 56, 28, 8, and 1.

We can set up our formula this way:

(a + b)^8 = (a^8 + 8a^7b + 28a^6b^2 + 56a^5b^3 + 70a^4b^4 + 56a^3b^5 + 28a^2b^6 + 8ab^7 + b^8)

We can plug our values for a and b into the equation to expand the binomial.

After plugging in our values, we're left with:

(y + 1)^8 = (y^8 + 8y^7 + 28y^6 + 56y^5 + 70y^4 + 56y^3 + 28y^2 + 8y + 1)

The reason the expanded value looks nearly identical to the formula is because our 2nd term is 1, and 1 raised to any power is equal to 1.