Binomial Expansion

I'm trying to calculate and I'm using
and expanding it to do so. I have got The question requires working it out to 2dp without a calculator. The calculations seem extremely laborious, so does anyone have any tips that will make it easier or a shortcut?

Thanks

Your expansion of $(1+x)^4$ is incorrect

Use Pascal's triangle - 1, 4, 6, 4,1

Sorry, my mistake and why do I need pascal's triangle for this?

Pascal's triangle gives the coefficients of each power of x and y in an expansion of a bracket, (x+y), to an integer (whole number) power.

You look at the line that is the power you're dealing with plus one So, for example, the 3rd line gives the coefficients for the power 2 - 1,2,1

$(x+y)^2 = x^2 + 2xy + y^2$

The fourth line gives them for the power 3 - 1,3,3,1

$(x+y)^3 = x^3 + 3x^2 y + 3xy^2 +y^3$

etc.

Notice the symmetry of the powers of x and y in the above expansions.

I've already expanded it?

Using the 5th line - 1,4,6,4,1

$(x+y)^4 = x^4 + 4x^3 y + 6x^2 y^2 + 4xy^3 + y^4$

Again, notice the symmetry of the powers.

How does this simplify in your case?

Using the 5th line - 1,4,6,4,1

$(x+y)^4 = x^4 + 4x^3 y + 6x^2 y^2 + 4xy^3 + y^4$

Again, notice the symmetry of the powers.

How does this simplify in your case?

Thanks

How come I'm told by my teachers to turn it into (1+x)^n before expanding?

For integer (whole number powers), you can do it either way.

Maybe they think you're less likely to make an error

Can you tell me why pascal's triangle does not work for natural number powers, but the general formula ( n(n-1)/2! ...) works?