Question

 

Phân tích đa thức thành nhân tử:

 

a) x² - 2xy + y² - m² + 2mn - n²

b) x² + 3cd .(2 - 3cd) - 10xy - 1 + 25y²

c) (4x² - 3x - 18)² - (4x² + 3x²)

d) 3a² - 6ab + 3b² - 12x²

^{giúp mik}

Answer 1

a) \(x^2-2xy+y^2-m^2+2mn-n^2\)

\(=\left(x^2-2xy+y^2\right)-\left(m^2-2mn+n^2\right)\)

\(=\left(x-y\right)^2-\left(m-n\right)^2\)

\(=\left[\left(x-y\right)-\left(m-n\right)\right]\left[\left(x-y\right)+\left(m-n\right)\right]\)

\(=\left(x-y-m+n\right)\left(x-y+m-n\right)\)

Answer 2

b) \(x^2+3cd\left(2-3cd\right)-10xy-1+25y^2\)

\(=\left(x^2-10xy+25y^2\right)+2.3cd-\left(3cd\right)^2-1\)

\(=\left(x-5y\right)^2-\left[\left(3cd\right)^2-2.3cd+1\right]\)

\(=\left(x-5y\right)^2-\left(3cd-1\right)^2\)

\(=\left[\left(x-5y\right)-\left(3cd-1\right)\right]\left[\left(x-5y\right)+\left(3cd-1\right)\right]\)

\(=\left(x-5y-3cd+1\right)\left(x-5y+3cd-1\right)\)

Answer 3

H

Answer 4

d) \(3a^2-6ab+3b^2-12x^2\)

\(=3\left(a^2-2ab+b^2-4x^2\right)\)

\(=3\left[\left(a^2-2ab+b^2\right)-\left(2x\right)^2\right]\)

\(=3\left[\left(a-b\right)^2-\left(2x\right)^2\right]\)

\(=3\left(a-b-2x\right)\left(a-b+2x\right)\)