b) 8a3 + 4a2b - 2ab2 – b3 = (8a3 – b3 ) + (4a2b - 2ab2 )

= (2a – b)(4a2 + 2ab + b2) + 2ab(2a – b)

= (2a – b)( 4a2 + 2ab + b2 + 2ab) = (2a – b)(2a + b)2

11: \(\dfrac{1}{3}x^2y^2\left(6x+\dfrac{2}{3}x^2-y\right)\)

\(=2x^3y^2+\dfrac{2}{9}x^4y^2-\dfrac{1}{3}x^2y^3\)

12: \(\dfrac{3}{4}x^3y^2\left(4x^2y-x+y^5\right)\)

\(=3x^5y^3-\dfrac{3}{4}x^4y^2+\dfrac{3}{4}x^3y^7\)

13: \(-5x^2y^4\left(3x^2y^3-2x^3y^2-xy\right)\)

\(=-15x^4y^7+10x^5y^6+5x^3y^5\)

a, 4\(x^3\).y + \(\dfrac{1}{2}\)yz

  =y.(4\(x^3\) + \(\dfrac{1}{2}\)z)

b, (a² + b² - 5)² - 2.(ab + 2)²

 = [a² + b² - 5  - \(\sqrt{2}\)(ab + 2) ].[ a² + b² - 5 + \(\sqrt{2}\)(ab +2)]

a) \(4x^3y+\dfrac{1}{2}yz=y\left(4x^3+\dfrac{1}{2}z\right)\)

b) \(\left(a^2+b^2-5\right)^2-2.\left(ab+2\right)^2\)

\(=\left[\left(a^2+b^2-5\right)+2\left(ab+2\right)\right]\left[\left(a^2+b^2-5\right)-2\left(ab+2\right)\right]\)

\(=\left[a^2+b^2-5+2ab+4\right]\left[a^2+b^2-5-2ab-4\right]\)

\(=\left[a^2+b^2+2ab-1\right]\left[a^2+b^2-2ab-9\right]\)

\(=\left[\left(a+b\right)^2-1\right]\left[\left(a-b\right)^2-9\right]\)

\(=\left[\left(a+b+1\right)\left(a+b-1\right)\right]\left[\left(a-b+3\right)\left(a-b-3\right)\right]\)

Mình đã làm sai, cô Hoài Thương đúng rồi.

1. x² - 6x + 9=(x-3)²

2. 25 +  10x + x²=(x+5)²

3. \(\dfrac{1}{4}a^2+2ab^2+4b^4=\left(\dfrac{1}{2}a+2b^2\right)^2\)

4.\(\dfrac{1}{9}-\dfrac{2}{3}y^4+y^8=\left(\dfrac{1}{3}-y^4\right)^2\)

5.x³ + 8y³=(x+8y)(x²-8xy+64y²)

6.8y³ -125=(2y-5)(4y²+10y+25)

7.a⁶-b³=(a²-b)(a⁴+a²b+b²)

8 x² - 10x + 25=(x-2)²

1) \(x^2-6x+9=\left(x-3\right)^2\)

2) \(25+10x+x^2=\left(5+x\right)^2\)

3) \(\dfrac{1}{4}a^2+2ab+4b^4=\left(\dfrac{1}{2}a+2b^2\right)^2\)

4) \(\dfrac{1}{9}-\dfrac{2}{3}y^4+y^8=\left(\dfrac{1}{3}-y^4\right)^2\)

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

6) \(8y^3-125=\left(2y-5\right)\left(4y^2+10y+25\right)\)

7) \(a^6-b^3=\left(a^2-b\right)\left(a^4+a^2b+b^2\right)\)

8) \(x^2-10x+25=\left(x-5\right)^2\)

9) \(8x^3-\dfrac{1}{8}=\left(2x-\dfrac{1}{2}\right)\left(4x^2+x+\dfrac{1}{4}\right)\)

a,\(2axy-4a^2xy^2+6a^3x^2\)

\(=2ax\left(y-2ay^2+3a^2x\right)\)

b,\(5a^2xy-10a^3x-15ay\)

\(=5a\left(axy-2ax-3y\right)\)

Tự lm tiếp, tất cả đều dùng bằng phương phép đặt nhân tử chung nhé

23) \(2axy-4a^2xy^2+6a^3x^2\)

\(=2ax\left(y-2ay^2+3a^2x\right)\)

24) \(5a^2xy-10a^3x-15ay\)

\(=5a\left(axy-2a^2x-3y\right)\)

25) \(mxy-m^2x+my\)

\(=m\left(xy-mx+y\right)\)

26) \(2mx-4m^2xy+6mx\)

\(=2mx\left(1-2my+3\right)\)

\(=4mx\left(2-my\right)\)

27) \(a^2b-2ab^2+ab\)

\(=ab\left(a-2b+1\right)\)

28) \(5a^2b-2ab^2+ab\)

\(=ab\left(5a-2b+1\right)\)

29) \(-3x^2y^3-6x^3y^2-x^2y^2\)

\(=-x^2y^2\left(3y+6x+1\right)\)

30) \(5x^2y^4-10x^4y^2+5x^2y^2\)

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

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

(a+2b²)² ct: a²+2ab+b²=(a+b)²

\(a^2+2ab^2+4b^4=\left(a+2b\right)^2-2ab^2=\left(a+2b-\sqrt{2ab^2}\right)\left(a+2b+\sqrt{2ab^2}\right)\)

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

phân tích đa thức sau thành nhân tử 
x³-x+3x²y+3xy²+y³-y
giúp câu này nữa nha

2: \(8xy-24xy+16x\)

\(=8x\cdot y-8x\cdot3y+8x\cdot2\)

\(=8x\left(y-3y+2\right)=8x\left(-2y+2\right)\)

\(=-16y\left(y-1\right)\)

3: \(xy-x=x\cdot y-x\cdot1=x\left(y-1\right)\)

11: \(2mx-4m2xy+6mx\)

\(=2mx-2my\cdot4y+2mx\cdot3\)

\(=2mx\left(1-4y+3\right)\)

\(=2mx\left(4-4y\right)=8mx\left(1-y\right)\)

12: \(7x^2y^5-14x^3y^4-21y^3\)

\(=7y^3\cdot x^2y^2-7y^3\cdot2x^3y-7y^3\cdot3\)

\(=7y^3\left(x^2y^2-2x^3y-3\right)\)

13: \(2\left(x-y\right)-a\left(x-y\right)\)

\(=2\cdot\left(x-y\right)-a\cdot\left(x-y\right)\)

\(=\left(x-y\right)\left(2-a\right)\)