Question

How do you expand `(a+2b)^4`?

Answer 1

`a^4+8a^3b+24a^2b^2+32ab^3+16b^4`

Explanation:

`"we can expand using the appropriate row of coefficients"`
`"from "color(blue)"Pascal's triangle"`

`"for " n=4" the coefficients are"`

`color(white)(xxxxxx)1color(white)(x)4color(white)(x)6color(white)(x)4color(white)(x)1`

`"with decreasing powers of "a" from "a^4toa^0`

`"and increasing powers of "2b" from "(2b)^0to(2b)^4`

`rArr(a+2b)^4`

`=1.a^4(2b)^0+4.a^3(2b)^1+6.a^2(2b)^2+4.a(2b)^3`
`color(white)(=)+1.(2b)^4`

`=a^4+8a^3b+24a^2b^2+32ab^3+16b^4`