Bài 1.
a) -2x²y(2x² - 3y + 5yz)
= (-2x²y).2x² + (-2x²y).(-3y) + (-2x²y).5yz
= -4x⁴y + 6x²y² - 10x²y²z
b) (6x³ - 7x² - x + 2) : (2x + 1)
= (6x³ - 6x² - x² + x - 2x + 2) : (2x + 1)
= [(6x³ - 6x²) - (x² - x) - (2x - 2)] : (2x + 1)
= [6x²(x - 1) - x(x - 1) - 2(x - 1)] : (2x + 1)
= [(x - 1)(6x² - x - 2)] : (2x + 1)
= [(x - 1)(6x² + 3x - 4x - 2)] : (2x + 1)
= {(x - 1)[(6x² + 3x) - (4x + 2)]} : (2x + 1)
= {(x - 1)[3x(2x + 1) - 2(2x + 1)]} : (2x + 1)
= [(x - 1)(2x + 1)(3x - 2)] : (2x + 1)
= (x - 1)(3x - 2)
Bài 2
a) 5x²y - 5xy²
= 5xy(x - y)
b) x² - 2x - y² + 1
= (x² - 2x + 1) - y²
= (x - 1)² - y²
= (x - y - 1)(x + y - 1)
c) x² - 6x + 9
= x² - 2.x.3 + 3²
= (x - 3)²
Bài 1c) (x - 2y)(3xy + 5y² + x)
= 3x²y + 5xy² + x² - 6xy² - 10y³ - 2xy
= 3x²y - xy² + x² - 10y³ - 2xy
