Lời giải:

a) (x2 + 2xy + y2) : (x + y)

= (x + y)2 : (x + y)

= x + y

b) (125x3 + 1) : (5x + 1)

= [(5x)3 + 1] : (5x + 1)

= (5x + 1)[(5x)2 – 5x + 1]] : (5x + 1)

= (5x)2 – 5x + 1

= 25x2 – 5x + 1

c) (x2 – 2xy + y2) : (y – x)

= (x – y)2 : [-(x – y)]

= -(x – y)

= y – x

Hoặc (x2 – 2xy + y2) : (y – x)

= (y2 – 2yx + x2) : (y – x)

= (y – x)2 : (y – x)

= y – x

\(\text{a) (x^2 + 2xy + y^2) : (x + y)}\\ \left(x+y\right)^2:\left(x+y\right)=x+y\)

a)x+y

b)25x²-5x+1

c)-x+y

=2x-1

h, \(27x^3-8=\left(3x-2\right)\left(9x^2+6x+4\right)\)

\(\Rightarrow\left(27x^3-8\right):\left(3x-2\right)\\ =\left(3x-2\right)\left(9x^2+6x+4\right):\left(3x-2\right)\\ =9x^2+6x+4\)

g, \(x^4-2x^2+1=\left(x^2-1\right)^2\)

\(\Rightarrow\left(x^4-2x^2+1\right):\left(1-x^2\right)\\ =\left(x^2-1\right)^2:\left(1-x^2\right)\\ =x^2-1\)

 (2x⁴-8x²+8) : (4-2x²)

=  2(x⁴-4x²+4) : 2(2-x²)

= (x⁴-4x²+4) : (2-x²)

= (x²  - 2) : (2-x²)

=   - 1

\(2x^4+8x^2+8=2\left(x^4+4x^2+4\right)=2\left(x^2+2\right)^2\)

\(\left(4-2x^2\right)=2\left(2-x^2\right)\Rightarrow\frac{2x^4+8x^2+8}{4-2x^2}=\frac{2\left(x^2+2\right)^2}{2\left(2-x^2\right)}=\frac{\left(x^2+2\right)^2}{2-x^2}\)

Nếu không sai đề thì tự phân tích rồi thực hiện phép chia đa thức

a: \(\left(4x^2+12xy+9y^2\right):\left(2x+3y\right)=\left(2x+3y\right)^2:\left(2x+3y\right)=2x+3y\)

d: \(\left(x^2+6xy+9y^2\right):\left(x+3y\right)=\left(x+3y\right)^2:\left(x+3y\right)=x+3y\)

e: \(\dfrac{64y^3-27}{4y-3}=\dfrac{\left(4y-3\right)\left(16y^2+12y+9\right)}{4y-3}=16y^2+12y+9\)

a, \(4x^2+12xy+9y^2=\left(2x+3y\right)^2\)

\(\Rightarrow\left(4x^2+12xy+9y^2\right):\left(2x+3y\right)\)

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

b,\(x^2+6xy+9y^2=\left(x+3y\right)^2\)

\(\Rightarrow\left(x^2+6xy+9y^2\right):\left(x+3y\right)\\ =\left(x+3y\right)^2:\left(x+3y\right)\\ =x+3y\)

c, \(64y^3-27=\left(4y-3\right)\left(16y^2+12y+9\right)\)

\(\Rightarrow\left(64x^3-27\right):\left(4y-3\right)\\ =\left[\left(4y-3\right)\left(16x^2+12x+9\right)\right]:\left(4y-3\right)\\ =16x^2+12x+9\)

(x2 – 2xy + y2) : (y – x)

= (x – y)2 : [-(x – y)]

= -(x – y)

= y – x

Hoặc (x2 – 2xy + y2) : (y – x)

= (y2 – 2yx + x2) : (y – x)

= (y – x)2 : (y – x)

= y – x

(x2 + 2xy + y2) : (x + y)

= (x + y)2 : (x + y)

= x + y

a) Kết quả - x 2  + 2.               b) Kết quả − 1 2 ( 4 x 2 + 10 x + 25 ) .  

c) Kết quả - ( x 3   +   1 ) 2 .

Ta có: \(\left(a+2b-3c-d\right)\left(a+2b+3c+d\right)\)

\(=\left[\left(a+2b\right)-\left(3c+d\right)\right]\cdot\left[\left(a+2b\right)+\left(3c+d\right)\right]\)

\(=\left(a+2b\right)^2-\left(3c+d\right)^2\)

\(=a^2+4ab+4b^2-9c^2-6cd-d^2\)

( a + 2b - 3c - d )( a + 2b + 3c + d )

= [ ( a + 2b ) - ( 3c + d ) ][ ( a + 2b ) + ( 3c + d ) ]

= ( a + 2b )² - ( 3c + d )²

= a² + 4ab + 4b² - ( 9c² + 6cd + d² )

= a² + 4ab + 4b² - 9c² - 6cd - d²

(a + 2b − 3c − d) (a + 2b + 3c + d) 

= [(a + 2b) − (3c + d) ] · [(a + 2b) + (3c + d)] 

= (a + 2b)² − (3c + d)² 

= a² + 4ab + 4b² − 9c² − 6cd − d²

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