Question

How do you use the binomial theorem to expand and simplify the expression `(5-3y)^3`?

Answer 1

`125-225y+135y^2-27y^3`

Explanation:

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

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

`"where the binomial coefficient "`

`""^nC_r=(n!)/(r!(n-r)!)`

`"we can obtain the coefficients using the appropriate row"`
`"of "color(blue)"Pascal's triangle ""for n = 3"`

`rArrcolor(red)(1)color(white)(x)color(red)(3)color(white)(x)color(red)(3)color(white)(x)color(red)(1)`

`"here "a=5" and "b=-3y`

`rArr(5-3y)^3`

`=color(red)(1).5^3(-3y)^0+color(red)(3).5^2(-3y)^1+color(red)(3).5^1(-3y)^2+color(red)(1).5^0(-3y)^3`

`=125-225y+135y^2-27y^3`