43. Phân tích các đa thức sau thành nhân tử:
a) x2 + 6x + 9; b) 10x – 25 – x2
c) 8x3 - \(\frac{1}{8}\); d) \(\frac{1}{25}\)x2 – 64y2
a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - \(\frac{1}{8}\) = (2x)3 – (\(\frac{1}{2}\))3 = (2x - \(\frac{1}{2}\))[(2x)2 + 2x . \(\frac{1}{2}\) + (\(\frac{1}{2}\))2]
= (2x - \(\frac{1}{2}\))(4x2 + x + \(\frac{1}{4}\))
d) \(\frac{1}{25}\)x2 – 64y2 = \(\left ( \frac{1}{5}x \right )^{2}\)- (8y)2 = (\(\frac{1}{5}\)x + 8y)(\(\frac{1}{5}\)x - 8y)