Question

Đề bài: Phân tích các đa thức thành nhân tử :

a) x² + 2xy + x + 2y

b) 7x² - 7xy - 5x + 5y

c) x² - 6x + 9 - 9y²

d) x³ - 3x² + 3x - 1 + 2 ( x² - x )

e) 15 ( x - y ) - 25x + 25y

f) 12x² - 3xy + 8xz - 2yz

y) x³ + x²y - x²z - xyz

Các cậu giúp tớ với nhé, tớ cảm ơn trước !

Answer 1

a) \(x^2+2xy+x+2y\)

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

\(=\left(x+2y\right)\left(x+1\right)\)

b) \(7x^2-7xy-5x+5y\)

\(=7x\left(x-y\right)-5\left(x-y\right)\)

\(=\left(x-y\right)\left(7x-5\right)\)

c) \(x^2-6x+9-9y^2\)

\(=\left(x^2-6x+9\right)-9y^2\)

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

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

d) \(x^3-3x^2+3x-1+2\left(x^2-x\right)\)

\(=\left(x^3-1\right)-\left(3x^2-3x\right)+2\left(x^2-x\right)\)

\(=\left(x-1\right)\left(x^2+x+1\right)-3x\left(x-1\right)+2x\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2+x+1-3x+2x\right)\)

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

e) \(15\left(x-y\right)-25x+25y\)

\(=15\left(x-y\right)-25\left(x-y\right)\)

\(=\left(15-25\right)\left(x-y\right)\)

\(=-10\left(x-y\right)\)

f) \(12x^2-3xy+8xz-2yz\)

\(=3x\left(4x-y\right)+2z\left(4x-y\right)\)

\(=\left(4x-y\right)\left(3x+2z\right)\)

y) \(x^3+x^2y-x^2z-xyz\)

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

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