Question

What is the standard form of `y=(x + 3)^3`?

Answer 1

`x^3+9x^2+27x+27`

Explanation:

`"Given " (x+a)(x+b)(x+c)" the expansion is"`

`=x^3+(a+b+c)x^2+(ab+bc+ac)x+abc`

`"now " (x+3)^3=(x+3)(x+3)(x+3)`

`"with " a=b=c=3`

`rArr(x+3)^3`

`=x^3+(3+3+3)x^2+(9+9+9)x+(3xx3xx3xx3)`

`=x^3+9x^2+27x+27`

Answer 2

`color(blue)(y=x^3+9x^2+27x+27)`

Explanation:

`y=(x+3)^3`

`color(white)(..........)x+3`
`color(white)(......) xx x+3`
`color(white)(............)overline(x^2+3x)`
`color(white)(..............)+3x+9`
`color(white)(...........)overline(x^2+6x+9)`
`color(white)(.......) xx x+3`
`color(white)(.............)overline(x^3+6x^2+9x)`
`color(white)(......................)3x^2+18x+27`
`color(white)(.............)overline(color(blue)(x^3+9x^2+27x+27)`