Question

Bài toán 2 : Phân tích đa thức sau thành nhân tử :

a) x⁴ – y⁴

b) x² – 3y²

c) (3x – 2y)² – (2x – 3y)²

d) 9(x – y)² – 4(x + y)²

e) (4x² – 4x + 1) – (x + 1)²

f) x³ + 27

g) 27x³ – 0,001

h) 125x³ – 1

GIÚP MÌNH vS hUhUhUHU :(((

Answer 1

a) \(^{x^4-y^4}\)

\(=\left(x^2-y^2\right)\left(x^2+y^2\right)\)

\(=\left[\left(x-y\right).\left(x+y\right)\right].\left(x^2-y^2\right)\)

\(=\left(x-y\right).\left(x+y\right).\left(x^2-y^2\right)\)

c) \(\left(3x-2y\right)^2-\left(2x-3y\right)^2\)

\(=\left[\left(3x-2y\right)+\left(2x-3y\right)\right].\left[\left(3x-2y\right)-\left(2x-3y\right)\right]\)

\(=\left(3x-2y+2x-3y\right)\left(3x-2y-2x+3y\right)\)

b) \(x^2-3y^2\)

\(=\left(x-3y\right)\left(x+3y\right)\)

d) \(9\left(x-y\right)^2-4\left(x+y\right)^2\)

\(=9\left(x-y\right)^2+4\left(x-y\right)^2\)

\(=\left(x-y\right).\left(9+4\right)\)

\(=\left(x-y\right).13\)

\(=13\left(x-y\right)\)

f) \(x^3+27\)

\(=x^3+3^3\)

\(=\left(x+3\right)\left(x^2-x.3+3^2\right)\)

h) \(125x^3-1\)

\(=\left(5x\right)^3-1^3\)

\(=\left(5x-1\right)\left(5x^2+5x.1+1^2\right)\)

\(=\left(5x-1\right)\left(5x^2+5x+1\right)\)

Answer 2

\(a,x^4-y^4=\left(x^2+y^2\right)\left(x^2-y^2\right)=\left(x^2+y^2\right)\left(x+y\right)\left(x-y\right)\)

\(b,x^2-3y^2=\left(x+\sqrt{3}y\right)\left(x-\sqrt{3}y\right)\)

cn lại tg tự nha bn

Answer 3

a, x⁴ - y⁴ 

= (x² - y²)(x² + y²)

= (x + y)(x - y)(x² + y²)

f, x³ + 27

= x³ + 3³ 

= (x + 3)(x² - 3x + 3²)

tớ k bt lm nx