Question

Factor completely x^2+9x+18 and Expand (a+3)^2

Answer 1

•   Factor x² + 9x + 18 completely:

In order to make the process easier, I'm going to try to find two integer numbers, so that

their sum is 9

their product is 18


Just search into the set of the divisors of 18

D(18) = {1, 2, 3, 6, 9, 18}


Take the numbers 3 and 6, and you verify that

3 + 6 = 9          ✔

3 × 6 = 18          ✔


So, rewrite conveniently 9x as 3x + 6x, and then factor the quadratic polynomial by grouping:

x² + 9x + 18

= x² + 3x + 6x + 18

= x² + 3x + 6x + 6 · 3

= x · (x + 3) + 6 · (x + 3)

= (x + 3) · (x + 6)          ✔

and that is the complete factorization of x² + 9x + 18.

_______________


•   Expand (a + 3)²:

Just apply the distributive property of multiplication, and you have

(a + 3)²

= (a + 3) · (a + 3)

= (a + 3) · a + (a + 3) · 3

= a · a + 3 · a + a · 3 + 3 · 3

= a² + 3a + 3a + 3²

= a² + 6a + 9     <———     this is the expanded form.


I hope this helps. =)