Question

What is the coefficient of $z$ in $(z-5{)}^3$?

• A. 125
• B. -25
• C. 5
• D. 75

Answer 1

The correct option is D

75

$(z-5{)}^3=z^3-5^3-3\times z^2\times 5+3\times z\times 5^2$

$\text{[Using}(a-b{)}^3=a^3-b^3-3a^{2}b+3a{b}^2$]

$\Rightarrow (z-5{)}^3$ = $z^3-125-15z^2+75z$

Hence, the coefficient of $z$ is 75.