Question

Got stuck on finding property “a” in said polynomial

Answer 1

Hence, in the simplification of
`(y -3)(y^2 +3y + 9)` the value of a = 9.

Explanation:

Here, the given expression is
`(y -3)(y^2 +3y + 9)`

Simplify this given expression, we get:

`(y -3)(y^2 +3y + 9)  = y)(y^2 +3y + 9)  -3(y^2 +3y + 9)\\= y(y^2) + y(3y)  + y(9)   -3(y^2) -3(3y) -3(9)\\=y^3 + 3y^2 + 9y - 3y^2 -9y  - 27\\\implies y^3  - 27  = 0\\`

Now, the given expanded form is
`y^3 + 3y^2 + ay - 3y^2 -ay  - 27`

Comparing it with given second last step in simplification, we get

`y^3 + 3y^2 + ay - 3y^2 -ay  - 27  = y^3 + 3y^2 + 9y - 3y^2 -9y  - 27`

Comparing all term on both sides, we get

ay = 9y

and -ay = -9y

⇒ a = 9 on both sides.

Hence, in the simplification of the polynomial, the value of a = 9.