How do you factor 36a2−48a+16?
1 Answer
Jan 28, 2016
4(3a−2)2
Explanation:
There is a 'common factor' of 4
hence 4 (
9a2−12a+4) To factor the trinomial:
9×4=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:
9a2−6a−6a+4 factor in pairs.
[9a2−6a]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 :
36a2−48a+16=4(3a−2)2
