Question

How do you use the binomial theorem to expand and simplify the expression `(x+2y)^4`?

Answer 1

`(x+2y)^4=x^4+8x^3y+24x^2y^2+32xy^3+16y^4`

Explanation:

Using Binomial expansion of `(x+2y)^4` as follows

`(x+2y)^4`

`=^4C_0x^4+^4C_1x^3(2y)+^4C_2x^2(2y)^2+^4C_3x(2y)^3+^4C_4(2y)^4`

`=x^4+4x^3(2y)+6x^2(4y^2)+4x(8y^3)+16y^4`

`=x^4+8x^3y+24x^2y^2+32xy^3+16y^4`