Question

How do you simplify `(2x + 3y)^3`?

Answer 1

`(2x+3y)=color(blue)(8x^3+36x^2y+54xy^2+27y^3)`

Explanation:

Using Pascal's Triangle to simplify the expansion:
#{: (ul("exponent")," | pattern:",,,,,,), (0,,1,,,,,), (1,,1,1,,,,), (2,,1,2,1,,,), (color(lime)3,,color(magenta)1,color(magenta)3,color(magenta)3,color(magenta)1,,), (4,,1,4,6,4,1,), (5,,1,5,10,10,5,1), (...,,...,,,,,) :}#

`(2x+3y)^color(lime)3`
`color(white)("XXX")=color(magenta)1 * (2x)^3 * (3y)^0+color(magenta)3 * (2x)^2 * (3y)^1 + color(magenta)3 * (2x)^1 * (3y)^2 + color(magenta)1 * (2x)^0 * (3y)^3`

`color(white)("XXX")=color(white)("XXXXXXX")8x^3 +color(white)("XXXXX")36x^2y +color(white)("XXXXX") 54xy^2+color(white)("XXXXX")27y^3`