Question

[nguyễn bảo anh]

Bài toán 1: Phân tích thành nhân tử.

a) 20x – 5y e) 4x²y – 8xy² + 10x²y²

b) 5x(x – 1) – 3x(x – 1) g) 20x²y – 12x³

c) x(x + y) – 6x – 6y h) 8x⁴ + 12x²y⁴ – 16x³y⁴

d) 6x³ – 9x² k) 4xy² + 8xyz

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

a) 3x(x +1) – 5y(x + 1) h) 3x³(2y – 3z) – 15x(2y – 3z)²

b) 3x(x – 6) – 2(x – 6) k) 3x(z + 2) + 5(-x – 2)

c) 4y(x – 1) – (1 – x) l) 18x²(3 + x) + 3(x + 3)

d) (x – 3)³ + 3 – x m) 14x²y – 21xy² + 28x²y²

e) 7x(x – y) – (y – x) n) 10x(x – y) – 8y(y – x)

Bài toán 3 : Tìm x biết.

a) 4x(x + 1) = 8(x + 1) g) 5x(x – 2000) – x + 2000 = 0

b) x(x – 1) – 2(1 – x) = 0 h) x² – 4x = 0

c) 2x(x – 2) – (2 – x)² = 0 k) (1 – x)² – 1 + x = 0

d) (x – 3)³ + 3 – x = 0 m) x + 6x² = 0

e) 5x(x – 2) – (2 – x) = 0 n) (x + 1) = (x + 1)²

Answer 1

[@Nk>↑@]

1.a)\(20x-5y=5\left(4x-y\right)\)

b)\(5x\left(x-1\right)-3x\left(x-1\right)=\left(5x-3x\right)\left(x-1\right)=2x\left(x-1\right)\)

c)\(x\left(x+y\right)-6x-6y=x\left(x+y\right)-6\left(x+y\right)=\left(x-6\right)\left(x+y\right)\)

d)\(6x^3-9x^2=3x^2\left(2x-3\right)\)

e)\(4x^2y-8xy^2+10x^2y^2=2xy\left(2x-8y+10xy\right)\)

g)\(20x^2y-12x^3=4x^2\left(5y-3x\right)\)

h)\(8x^4+12x^2y-16x^3y^4=4x^2\left(2x^2+12y-16xy^4\right)\)

Answer 2

[@Nk>↑@]

2.a)\(3x\left(x+1\right)-5y\left(x+1\right)=\left(3x-5y\right)\left(x+1\right)\)

b)\(3x\left(x-6\right)-2\left(x-6\right)=\left(3x-2\right)\left(x-6\right)\)

c)\(4y\left(x-1\right)-\left(1-x\right)=4y\left(x-1\right)+\left(x-1\right)=\left(4y+1\right)\left(x-1\right)\)

d)\(\left(x-3\right)^3+3-x=\left(x-3\right)^3-\left(x-3\right)=\left(x-3\right)\left[\left(x-3\right)^2-1\right]=\left(x-3\right)\left(x-2\right)\left(x-4\right)\)

e)\(7x\left(x-y\right)-\left(y-x\right)=7x\left(x-y\right)+\left(x-y\right)=\left(7x+1\right)\left(x-y\right)\)

h)\(3x^3\left(2y-3z\right)-15x\left(2y-3z\right)^2=3x\left(2y-3z\right)\left[x^2-5\left(2y-3z\right)\right]\)

k)Sai đề: \(3x\left(z+2\right)+5\left(-z-2\right)=3x\left(z+2\right)-5\left(z+2\right)=\left(3x-5\right)\left(z+2\right)\)

l)\(18x^2\left(3+x\right)+3\left(x+3\right)=3\left(x+3\right)\left(6x^2+1\right)\)

m)\(14x^2y-21xy^2+28x^2y^2=7xy\left(2x-3y+4xy\right)\)

n)\(10x\left(x-y\right)-8y\left(y-x\right)=10x\left(x-y\right)+8y\left(x-y\right)=2\left(5x+4y\right)\left(x-y\right)\)