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

1 Answer
Nov 18, 2015

#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#