Answer
$z^{3} - 5z^{2} + 13z - 9$
Work Step by Step
To simplify the polynomial we apply the distributive property that states:
a(b+c)=ab+ac
= $z(z^{2}-4z+9) - 1(z^{2}-4z+9)$
= ($z \times z^{2}$) + ($z \times -4z$) + ($ z\times 9$) + ($-1 \times z^{2}$) + ($-1 \times -4z$) + ($ -1 \times 9$)
= $z^{3} - 4z^{2} + 9z - 1z^{2} + 4z - 9$
= $z^{3} - 1z^{2} - 4z^{2} + 9z + 4z - 9$
= $z^{3} - 5z^{2} + 13z - 9$
We add like terms to get final answer
