Factor the expression 81z-18z^2+-1

 Exercise

$81z-18z^2-1$

 

Use the complete the square method to factor the trinomial of the form $ax^2+bx+c$. Take common factor $a$ ($-18$) to all terms

$-18\left(z^2-\frac{9}{2}z+\frac{1}{18}\right)$

 

Add and subtract $\displaystyle\left(\frac{b}{2a}\right)^2$

$-18\left(z^2-\frac{9}{2}z+\frac{1}{18}+\frac{81}{16}-\frac{81}{16}\right)$

 

Factor the perfect square trinomial $z^2+-\frac{9}{2}z+\frac{81}{16}$

$-18\left(\left(z- \frac{9}{4}\right)^2+\frac{1}{18}-\frac{81}{16}\right)$

 

Multiply the fraction and term in $- \frac{9}{4}$

$-18\left(\left(z-\frac{9}{4}\right)^2+\frac{1}{18}-\frac{81}{16}\right)$

 

Solve the product $-18\left(\left(z-\frac{9}{4}\right)^2+\frac{1}{18}-\frac{81}{16}\right)$

$-18\left(z-\frac{9}{4}\right)^2-18\cdot \left(\frac{1}{18}-\frac{81}{16}\right)$

$-18\left(z-\frac{9}{4}\right)^2-18\cdot \left(\frac{1}{18}-\frac{81}{16}\right)$

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