Question

How do you factor the trinomial `18a^2+48a+32`?

Answer 1

`2(3a+4)^2`

Explanation:

`18a^2 + 48a + 32`

• First reduce it to the smallest terms
• They are all divisible by 2

`(18a^2)/2 + (48a)/2 + 32/2`

`9a^2 + 24a + 16`

16(last term) x 9(co-efficient of `a^2`) = 144

• Think of two numbers that
  `rArr` When you multiply them = 144
  `rArr` When you add them = 24 (co-efficient of `a`)

• 12 and 12
  `rArr` 12 x 12 = 144
  `rArr` 12 + 12 = 24

• Replace the middle number with 12 and 12
  `9a^2 + 12a + 12a + 16`

• Split the expression
  `9a^2 + 12a----- | ----- + 12a + 16`

• Factorise the two
  `3a(3a + 4) + 4(3a +4)`

• Common factors so group
  `(3a + 4)(3a +4)`

`rArr` `(3a+4)^2`

• Remember we divided by 2
  `rArr` `2(3a+4)^2`