1) \(4x^5y^2-8x^4y^2+4x^3y^2\)

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

\(=4x^3y^2\left(x^2-2\cdot x\cdot1+1^2\right)\)

\(=4x^3y^2\left(x-1\right)^2\)

2) \(5x^4y^2-10x^3y^2+5x^2y^2\)

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

\(=5x^2y^2\left(x^2-2\cdot x\cdot1+1^2\right)\)

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

3) \(12x^2-12xy+3y^2\)

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

\(=3\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)

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

4) \(8x^3-8x^2y+2xy^2\)

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

\(=2x\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)

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

5) \(20x^4y^2-20x^3y^3+5x^2y^4\)

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

\(=5x^2y^2\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)

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

1: 4x^5y^2-8x^4y^2+4x^3y^2

=4x^3y^2(x^2-2x+1)

=4x^3y^2(x-1)^2

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

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

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

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

a: \(\dfrac{-6x^3y^4+4x^4y^3}{2x^3y^3}\)

\(=\dfrac{-6x^3y^4}{2x^3y^3}+\dfrac{4x^4y^3}{2x^3y^3}\)

\(=-3y+2x\)

b: \(\dfrac{5x^4y^2-x^3y^2}{x^3y^2}=\dfrac{5x^4y^2}{x^3y^2}-\dfrac{x^3y^2}{x^3y^2}\)

\(=5x-1\)

c: \(\dfrac{27x^3y^5+9x^2y^4-6x^3y^3}{-3x^2y^3}\)

\(=-\dfrac{27x^3y^5}{3x^2y^3}-\dfrac{9x^2y^4}{3x^2y^3}+\dfrac{6x^3y^3}{3x^2y^3}\)

\(=-9xy^2-3y+2x\)

a) \(\dfrac{-6x^3y^4+4x^4y^3}{2x^3y^3}\)

\(=\dfrac{2x^3y^3\cdot\left(-3y+2x\right)}{2x^3y^3}\)

\(=-3y+2x\)

\(=2x-3y\)

b) \(\dfrac{5x^4y^2-x^3y^2}{x^3y^2}\)

\(=\dfrac{5x\cdot x^3y^2-x^3y^2\cdot1}{x^3y^2}\)

\(=\dfrac{x^3y^2\cdot\left(5x-1\right)}{x^3y^2}\)

\(=5x-1\)

c) \(\dfrac{27x^3y^5+9x^2y^4-6x^3y^3}{-3x^2y^3}\)

\(=\dfrac{-3x^2y^3\cdot-9xy^2+-3x^2y^3\cdot-3y+-3x^2y^3\cdot2x}{-3x^2y^3}\)

\(=\dfrac{-3x^2y^3\cdot\left(-9xy^2-3y+2x\right)}{-3x^2y^3}\)

\(=-9xy^2-3x+2x\)

5.

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

\(=4x^3y^2(x+y)^2\)

9.

\(4x^5y^2+16x^4y^2-6x^3y^2=2x^3y^2(2x^2+4x-3)\)

13.

\(-3x^4y+6x^3y-3x^2y=-3x^2y(x^2-2x+1)=-3x^2y(x-1)^2\)

17.

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

\(=2x[(2x)^2-2.2x.y+y^2]=2x(2x-y)^2\)

21.

\((a^2+4)^2-16a^2b^2=(a^2+4)^2-(4ab)^2\)

\(=(a^2+4-4ab)(a^2+4+4ab)\)

25.

\(100a^2-(a^2+25)^2=(10a)^2-(a^2+25)^2\)

\(=(10a-a^2-25)(10a+a^2+25)\)

\(=-(a^2-10a+25)(a^2+10a+25)=-(a-5)^2(a+5)^2\)

29.

\(25a^2b^2-4x^2+4x-1=25a^2b^2-(4x^2-4x+1)\)

\(=(5ab)^2-(2x-1)^2=(5ab-2x+1)(5ab+2x-1)\)

33.

\(1-2m+m^2-x^2-4x-4=(m^2-2m+1)-(x^2+4x+4)\)

\(=(m-1)^2-(x+2)^2=[(m-1)-(x+2)][(m-1)+(x+2)]\)

\(=(m-x-3)(m+x+1)\)

37.

\(ax^2+bx^2+2xy(a+b)+ay^2+by^2\)

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

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

41.

\(5a^2-5=5(a^2-1)=5(a^2-1^2)=5(a-1)(a+1)\)

Answer:

\(2x^3+4x^2y+2xy^2\)

\(= 2 x ( x ² + 2 x y + y ² )\)

\(= 2 x ( x + y ) ² \)

\( − 3 x ^4 y − 6 x ^3 y ^2 − 3 x ^2 y ^3 \)

\(=-3x^2y(x^2+2xy+y^2)\)

\(=-3x^2y(x+y)^2\)

\(4x^5y^2+8x^4y^3+4x^3y^4\)

\(=4x^3y^2.x^2+4x^3y^2.2xy+4x^3y^2.y^2\)

\(=4x^3y^2.(x^2+2xy+y^2)\)

\(=4x^3y^2.(x+y)^2\)

đề bài là rút gọn à

a) x² + 6x + 8

= x² + 2x + 4x + 8

= (x² + 2x) + (4x + 8)

= x(x + 2) + 4(x + 8)

= (x + 2)(x + 4)

b) 3x² - 2(x - y)² - 3y²

= (3x² - 3y²) - 2(x - y)²

= 3(x² - y²) - 2(x - y)²

= 3(x + y)(x - y) - 2(x - y)²

= (x - y)[3(x + y) - 2(x - y)]

= (x - y)(3x + 3y - 2x + 2y)

= (x - y)(x + 5y)

c) 4x² - 9y² + 4x - 6y

= (4x² - 9y²) + (4x - 6y)

= (2x - 3y)(2x + 3y) + 2(2x - 3y)

= (2x - 3y)(2x + 3y + 2)

d) x(x + 1)² + x(x - 5) - 5(x + 1)²

= [x(x + 1)² - 5(x + 1)²] + x(x - 5)

= (x + 1)²(x - 5) + x(x - 5)

= (x - 5)[(x + 1)² + x]

= (x - 5)(x² + 2x + 1 + x)

= (x - 5)(x² + 3x + 1)

e) 2xy - x² + 3y² - 4y + 1

= -x² + 2xy - y² + 4y² - 4y + 1

= -(x² - 2xy + y²) + (4y² - 4y + 1)

= -(x - y)² + (2y - 1)²

= (2y - 1)² - (x - y)²

= (2y - 1 - x + y)(2y - 1 + x - y)

= (3y - x - 1)(x + y - 1)

f) 4x¹⁶ + 81

= (2x⁸)² + 2.2x⁸.9 + 9² - 2.2x⁸.9

= (2x⁸ + 9)² - 36x⁸

= (2x⁸ + 9) - (6x⁴)²

= (2x⁸ + 9 - 6x⁴)(2x⁸ + 9 + 6x⁴)

= (2x⁸ - 6x⁴ + 9)(2x⁸ + 6x⁴ + 9)