## Intermediate Algebra (6th Edition)

$(3a-5)^2$
The two numbers whose product is $ac= 9(25)=225$ and whose sum is $b= -30$ are $\{ -15,-15 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $9a^2-30a+25$, is \begin{array}{l}\require{cancel} 9a^2-15a-15a+25 \\\\= (9a^2-15a)-(15a-25) \\\\= 3a(3a-5)-5(3a-5) \\\\= (3a-5)(3a-5) \\\\= (3a-5)^2 .\end{array}