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

2 Answers
Jim G.
Apr 30, 2017

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

Barney V.
Apr 30, 2017

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)

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