How do you factor #36a^2-48a+16#?
1 Answer
Jan 28, 2016
# 4(3a - 2)^2#
Explanation:
There is a 'common factor' of 4
hence 4 (
#9a^2 - 12a + 4) # To factor the trinomial:
# 9 xx 4 = 36 # Consider factors of 36 which also sum to -12
Factors of 36: 1,2,3,4,6,9,12, 18 and 36 ( and their negatives )
The 'pair' which sum to -12 are -6 and -6
so trinomial becomes:
# 9a^2 - 6a - 6a + 4# factor in pairs.
#[9a^2 - 6a ] and [ -6a + 4 ]# hence 3a(3a - 2) and -2 (3a - 2 )
There is a common factor of (3a - 2 )
so (3a - 2 )(3a - 2 ) are the factors of the trinomial.
Putting all this together to obtain :
# 36a^2 - 48a + 16 = 4 (3a - 2 )^2#