Question
Solve:
$(z - 6)(z + 2)$
$(z - 6)(z + 2)$
✓
Answer
$= z^2- 4z - 12$
$\Big[$Adding and subtracting $\Big(\frac{4}{2}\Big)^2\Big]$
$=\text{z}^2-4\text{z}+\Big(\frac{4}{2}\Big)^2-\Big(\frac{4}{2}\Big)^2-12$
$=\text{z}^2-4\text{z}=(2)^2-(2)^2-12$
$=(\text{z}-2)^2-16$
Comleting the squares
$=(\text{z}-2)^2-(4)^2$
$=[(\text{z}-2)-4][(\text{z}-2)+4]$
$=(\text{z}-6)(\text{z}+2)$
$\Big[$Adding and subtracting $\Big(\frac{4}{2}\Big)^2\Big]$
$=\text{z}^2-4\text{z}+\Big(\frac{4}{2}\Big)^2-\Big(\frac{4}{2}\Big)^2-12$
$=\text{z}^2-4\text{z}=(2)^2-(2)^2-12$
$=(\text{z}-2)^2-16$
Comleting the squares
$=(\text{z}-2)^2-(4)^2$
$=[(\text{z}-2)-4][(\text{z}-2)+4]$
$=(\text{z}-6)(\text{z}+2)$
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