Chapter 7 - Polynomial Equations and Factoring - 7.3 - Special Products of Polynomials - Exercises - Page 376: 45

$k=64$

The square of a binomial $a-b$ is equal to $(a-b)^{2}=a^{2}-2ab+b^{2}$ Comparing $9x^{2}-48x+k$ with $a^{2}-2ab+b^{2}$, we have $a^{2}=9x^{2}\implies a=3x$ $2ab=48x\implies b=\frac{48x}{2a}=\frac{48x}{2(3x)}=8$ $ k=b^{2}=64$