Question

Phân tích các đa thức sau thành nhân tử :

\(\left(7x-4\right)^2-\left(2x+1\right)^2\)

\(49.\left(y-4\right)^{^{ }2}-9.\left(y+2\right)^2\)

\(8x^3+\dfrac{1}{27}\)

125 -\(x^6\)

Answer 1

(7x - 4)² - (2x + 1)²

= (7x - 4 - 2x - 1)(7x - 4 + 2x + 1)

= (5x - 5)(9x - 3)

= 5(x - 1).3.(3x - 1)

= 15(x - 1)(3x - 1)

49(y - 4)² - 9(y + 2)²

= [7(y - 4)]² - [3(y + 2)]²

= (7y - 28)² - (3y + 6)²

= (7y - 28 + 3y + 6)(7y - 28 - 3y - 6)

= (10y - 22)(4y - 34)

= 2.(5y - 11).2.(2y - 17)

= 4(5y - 11)(2y - 17)

8x³ + \(\dfrac{1}{27}\)

= (2x)³ + (\(\dfrac{1}{3}\))³

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

125 - x⁶

= 5³ - (x²)³

= (5 - x²)(25 + 5x² + x⁴)

= (\(\sqrt{5}+x\))(\(\sqrt{5}-x\))(25 + 5x² + x⁴)