第4章 4.15

(1)

$(x-3)(x-3) = x^2 - 6x + 9$

(2)

$\left(x-\frac{1}{2}\right)\left(x+\frac{1}{3}\right) = x^2 - \frac{1}{6}x - \frac{1}{6}$

(3)

$(x-3+\sqrt{2})(x-3-\sqrt{2}) = x^2 - (3-\sqrt{2}+3+\sqrt{2})x + (3+\sqrt{2})(3-\sqrt{2}) = x^2 - 6x + (9-2) = x^2 - 6x + 7$

(4)

$(x-4+3\sqrt{3}i)(x-4-3\sqrt{3}i) = x^2 - (4-3\sqrt{3}i+4+3\sqrt{3}i)x + (4-3\sqrt{3}i)(4+3\sqrt{3}i) = x^2 - 8x + (16+27)$ $= x^2 - 8x + 43$

(5)

$\left(x-\frac{-5-2\sqrt{5}i}{3}\right)\left(x-\frac{-5+2\sqrt{5}i}{3}\right) = x^2 - \left(\frac{-5-2\sqrt{5}i}{3}+\frac{-5+2\sqrt{5}i}{3}\right)x + \left(\frac{-5-2\sqrt{5}i}{3}\right)\left(\frac{-5+2\sqrt{5}i}{3}\right)$ $= x^2 + \frac{10}{3}x + 5$