By expanding both sides of the identity (1+x)^3 = (1+x)^3 (1+x)^2, show that 5C2 = 3C2 + 3C1*2C1 + 3C0*2C2

[OddDog]

Hi, can someone help me with these questions

I've expanded both sides and got 1+3x+3x^2+x^3 = 1+5x+10x^2+10x^3+5x^4+x^5 which I know is (1+x)^5
But which part of RHS does 5C2 come from and what part of LHS does the other part of the combinatoric equation come from?

For the second question, I've expanded the two brackets separately in RHS and kept the coefficients in combinatoric form but how would I go about multiplying the two brackets together

 

[blamocur]

I've expanded both sides and got 1+3x+3x^2+x^3 = 1+5x+10x^2+10x^3+5x^4+x^5

Why is this an identity?

 

[Harry_the_cat]

Pretty sure the LHS should be \(\displaystyle (1+x)^5\).

When you expand it leave the coefficients in \(\displaystyle \begin{bmatrix}a\\b\end{bmatrix}\) form.

And leave the RHS as the product of a cubic and a quadratic.