Question

How do you expand `(x-3y)^4`?

Answer 1

`x^4-12x^3y+54x^2y^2-108xy^3+81y^4`

Explanation:

`"expand using the "color(blue)"binomial theorem"`

`•color(white)(x)(a+b)^n=sum_(r=0)^n((n),(r))a^(n-r)b^r`

`"where "((n),(r))=(n!)/(r!(n-r)!)`

`"the coefficients can be generated using the appropriate"`
`"row of "color(blue)"Pascal's triangle"`

`"for n =4 the row of coefficients is"`

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

`"here " a=x" and " b=-3y`

`rArr(x-3y)^4`

`=1.x^4(-3y)^0+4.x^3(-3y)^1+6.x^2(-3y)^2+4.x^1(-3y)^3+1.x^0(-3y)^4`

`=x^4-12x^3y+54x^2y^2-108xy^3+81y^4`