1) 4x³ - 16x
= 4x(x² - 4)
= 4x(x - 2)(x + 2)
2) x⁴ - y⁴
= (x² - y²)(x² + y²)
= (x - y)(x + y)(x² + y²)
3) x² - 6x + 9 - y²
= (x² - 6x + 9) - y²
= (x - 3)² - y²
= (x - y - 3)(x + y - 3)
4) x² - 4x - 5
= x² - 4x + 4 - 9
= (x² - 4x + 4) - 3²
= (x - 2)² - 3²
= (x - 2 - 3)(x - 2 + 3)
= (x - 5)(x + 1)
5) x² - 9x + 20
= x² - 4x - 5x + 20
= (x² - 4x) - (5x - 20)
= x(x - 4) - 5(x - 4)
= (x - 4)(x - 5)
6) xy² + x²y + 1/4 y³
= y(x² + xy + 1/4 y²)
= y(x + y/2)²
7) x³ - y⁶
= x³ - (y²)³
= (x - y²)(x² + xy² + y⁴)
8) x² + 2xy - 4x - 8y
= (x² + 2xy) - (4x + 8y)
= x(x + 2y) - 4(x + 2y)
= (x + 2y)(x - 4)
9) 3x² + 3x - 6
= 3(x² + x - 6)
= 3(x² - 2x + 3x - 6)
= 3[(x² - 2x) + (3x - 6)]
= 3[x(x - 2) + 3(x - 2)]
= 3(x - 2)(x + 3)
10) 3x² - 4x - 7
= 3x² + 3x - 7x - 7
= (3x² + 3x) - (7x - 7)
= 3x(x + 1) - 7(x + 1)
= (x + 1)(3x - 7)
11) Ta có:
49y² + 28y + 4
= (7y)² + 2.7y.2 + 2²
= (7y + 2)²
Vậy độ dài cạnh hình vuông là 7y + 2
