Question

1.Phân tích các đa thức sau thành nhân tử

a,5x-15y b,\(\dfrac{3}{5}\) x²+5x⁴-x²-y

c,14x²y²-21xy²+28x²y d,\(\dfrac{2}{7}\) x(3y-1)-\(\dfrac{2}{7}\) y(3y-1)

e,x³-3x²+3x-1 f,(x+y)²-4x²

g,27x³+\(\dfrac{1}{8}\) h,(x+y)³-(x-y)³

Answer 1

a) 5x - 15y = 5(x - 3y)

b) \(\dfrac{3}{5}\)x² + 5x⁴ - x² - y

= \(\dfrac{3}{5}\)x² + 5x².x² - x² - y

= x²(\(\dfrac{3}{5}\) + 5x² -1) - y

c) 14x²y² - 21xy² + 28x²y

= 7xy.xy - 7xy.3y + 7xy.4x

= 7xy(xy - 3y + 4x)

= 7xy[(xy - 3y) + 4x]

= 7xy[y(x - 3) +4x]

d) \(\dfrac{2}{7}x\)(3y - 1) - \(\dfrac{2}{7}y\)(3y - 1)

= (3y - 1).(\(\dfrac{2}{7}x\) - \(\dfrac{2}{7}y\) )

= (3y - 1).[\(\dfrac{2}{7}\)(x - y)]

e) x³ - 3x² + 3x - 1

= x².x - 3x.x + 3.x - 1

= x(x²-3x+3) - 1

g) 27x³ + \(\dfrac{1}{8}\)

= (3x)³ + \(\left(\dfrac{1}{2}\right)^3\)

= (3x + \(\dfrac{1}{2}\)).(9x² - \(\dfrac{3}{2}\)x + \(\dfrac{1}{4}\))

h) (x+y)³ - (x-y)³

= 2(3x²y) + 2y³

f) (x+y)² - 4x²

= -3x² + y(2x + y)