Question

Bài 1: Phân tích các đa thức sau thành nhân tử

a) 7x²y + 21xy - 14x

b) x² - xy + 5(x - y)

Bài 2: Thực hiện các phép tính

a) x(3 - x) + (x + 1)(x - 1)

b) (x - 1)(x² + x + 1) + 10

c) (5x³y² - 20x4y + 15x²y²) : 5x²y

d) (2x - 4 / x - 1) + (2x + 2 / x² - 1)

Answer 1

Bài 1:

\(a.7x^2y+21xy-14x\\ =7x\left(xy+3y-2\right)\)

\(b.x^2-xy+5\left(x-y\right)\\ =x\left(x-y\right)+5\left(x-y\right)\\ =\left(x-y\right)\left(x+5\right)\)

Answer 2

Bài 2:

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

\(b.\left(x-1\right)\left(x^2+x+1\right)+10\\ =x^3-1+10\\ =x^3+9\)

\(c.\left(5x^3y^2-20x^4y+15x^2y^2\right):5x^2y\\ =xy-4x^2+3y\)

\(d.\frac{2x-4}{x-1}+\frac{2x+2}{x^2-1}\\ =\frac{\left(2x-4\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}+\frac{2x+2}{\left(x-1\right)\left(x+1\right)}\\ =\left(2x-4\right)\left(x+1\right)+\left(2x+2\right)\\ =2x^2+2x-4x-4+2x+2\\ =2x^2-2\)

Answer 3

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