Answer:
(5a−3)^2
Step-by-step explanation:
25a^2 - 30a + 9
Factor the expression by grouping. First, the expression needs to be rewritten as 25a^2+pa+qa+9. To find p and q, set up a system to be solved.
p+q=−30
pq=25×9=225
Since pq is positive, p and q have the same sign. Since p+q is negative, p and q are both negative. List all such integer pairs that give product 225.
−1,−225
−3,−75
−5,−45
−9,−25
−15,−15
Calculate the sum for each pair.
−1−225=−226
−3−75=−78
−5−45=−50
−9−25=−34
−15−15=−30
The solution is the pair that gives sum −30.
p=−15
q=−15
Rewrite 25a^2 - 30a + 9 as (25a^2−15a)+(−15a+9).
(25a^2−15a)+(−15a+9)
Factor out 5a in the first and −3 in the second group.
5a(5a−3)−3(5a−3)
Factor out common term 5a−3 by using distributive property.
(5a−3)(5a−3)
Rewrite as a binomial square.
(5a−3)^2
