Question

Expand `(x^2+3y)^7` using Pascal's triangle ?

Answer 1

`x^14 + 21x^12y + 189x^10y^2 + 945x^8y^3 + 2835x^6y^4 + 5103x^4y^5 + 5103x^2y^6+ 2187y^7`

Explanation:

Pascal triangle gives us the coefficients in the binomial expansion; the terms up to 7 are;

So the expansion is:

`(x^2+3y)^7 = (1)(x^2)^7(3y)^0 + (7)(x^2)^6(3y)^1 + (21)(x^2)^5(3y)^2 +`
`" " (35)(x^2)^4(3y)^3 + (35)(x^2)^3(3y)^4 + (21)(x^2)^2(3y)^5 +`
`" " (7)(x^2)^1(3y)^6+ (1)(x^2)^0(3y)^7`

`" " = x^14 + 7x^12(3y) + 21x^10(9y^2) +`
`" " 35x^8(27y^3) + 35x^6(81y^4) + 21x^4(243y^5) +`
`" " 7x^2(729y^6)+ 2187y^7`

`" " = x^14 + 21x^12y + 189x^10y^2 +`
`" " 945x^8y^3 + 2835x^6y^4 + 5103x^4y^5 +`
`" " 5103x^2y^6+ 2187y^7`