(1+x)^8

To expand the expression (1+x)^8, we can use the binomial theorem. The formula for expanding (a + b)^n is:

(a + b)^n = C(n,0)a^nb^0 + C(n,1)*a^(n-1)*b^1 + C(n,2)*a^(n-2)*b^2 + ... + C(n,n)a^0b^n

where C(n,k) represents the binomial coefficient "n choose k".

For (1+x)^8, we have a=1, b=x, and n=8. Therefore, the expanded form is:

(1+x)^8 = C(8,0)1^8x^0 + C(8,1)1^7x^1 + C(8,2)1^6x^2 + C(8,3)1^5x^3 + C(8,4)1^4x^4 + C(8,5)1^3x^5 + C(8,6)1^2x^6 + C(8,7)1^1x^7 + C(8,8)1^0x^8

Now, we can calculate the binomial coefficients using the formula:

C(n,k) = n! / (k! * (n-k)!)

Plugging in the values and simplifying, we get:

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

Therefore, the expansion of (1+x)^8 is: 1 + 8x + 28x^2 + 56x^3 + 70x^4 + 56x^5 + 28x^6 + 8x^7 + x^8.