## Intermediate Algebra (6th Edition)

$(5a-6)^2$
Let $z=(5a-3)$. Then the given expression, $(5a-3)^2-6(5a-3)+9$, is equivalent to \begin{array}{l} z^2-6z+9 .\end{array} The two numbers whose product is $ac= 1(9)=9$ and whose sum is $b= -6$ are $\{ -3,-3 \}$. Using these two numbers to decompose the middle term of the expression, $z^2-6z+9$, results to \begin{array}{l} z^2-3z-3z+9 \\\\= (z^2-3z)-(3z-9) \\\\= z(z-3)-3(z-3) \\\\= (z-3)(z-3) \\\\= (z-3)^2 .\end{array} Since $z=(5a-3)$, then, \begin{array}{l} (z-3)^2 \\\\= (5a-3-3)^2 \\\\= (5a-6)^2 .\end{array}