\(a,x^2+7x+7y-y^2\)

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

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

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

\(b,x^2-2x-9y^2+6y\)

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

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

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

\(c,x^2-xy+x^3-3x^{2y}+3x^{2y}-y^3\)

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

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

Trả lời:

1, 15x + 15y = 15 ( x + y )

2, 8x - 12y = 4 ( 2x - 3y )

3, xy - x = x ( y - 1 )

4, x² + x = x ( x + 1 )

5, 3x²y - 8xy² = xy ( 3x - 8y )

6, 6x - 12xy - 18x² = 6x ( 1 - 2y - 3x )

1) 15x + 15y = 15(x + y)

2) 8x - 12y = 4(2x - 3y)

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

4) x² + x = x(x + 1) 

5) 3x²y - 8xy² = xy(3x - 8y)

6) 6x - 12xy - 18x² = 6x(1 - 2y - 3x) 

1.\(15x+15y=15\left(x+y\right)\)

2.\(8x-12y=4\left(2x-3y\right)\)

3.\(xy-x=x\left(y-1\right)\)

4.\(x^2+x=x\left(x+1\right)\)

5.\(3x^{2y}-8xy^2\)hay là \(\left(3x\right)^{2y}-\left(8xy\right)^2\)??

6.\(6x-12xy-18x^2=6x\left(1-2y-3x\right)\)

\(xy+3x-2y-6=-2\)

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

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

Vì x;y thuốc Z => y+3;x-2 thuộc Z

=>(y+3);(x-2) thuộc ước của 2

Ta có bảng sau

x-2       -1         1         2         -2

y+3      -2         2         1          -1

x          1          3         4         0

y          -5         -1        -2         -4

=> (x;y) thuộc { (1;-5); (3;-1); (4;-2); (0;-4)}

y

,(3x-1) mũ 2=9/16
<=> (3x-1)^2 = ( ±3/4)^2
<=> l3x-1l  = 3/4
Hoặc 3x-1 = 3/4
 <=> 3x= 3/4 + 1
<=> x = 7/4 : 3
<=> x= 7/1

a) ( 5x - y )( 25x² + 5xy + y² ) = ( 5x )³ - y³ = 125x³ - y³

b) ( x - 3 )( x² + 3x + 9 ) - ( 54 + x³ ) = x³ - 3³ - 54 - x³ = -27 - 54 = -81

c) ( 2x + y )( 4x² - 2xy + y² ) - ( 2x - y )( 4x² + 2xy + y² ) = ( 2x )³ + y³ - [ ( 2x )³ - y³ ]= 8x³ + y³ - 8x³ + y³ = 2y³

d) ( x + y )² + ( x - y )² + ( x + y )( x - y ) - 3x² = x² + 2xy + y² + x² - 2xy + y² + x² - y² - 3x² = y²

e) ( x - 3 )³ - ( x - 3 )( x² + 3x + 9 ) + 6( x + 1 )²

= x³ - 9x² + 27x - 27 - ( x³ - 3³ ) + 6( x² + 2x + 1 )

= x³ - 9x² + 27x - 27 - x³ + 27 + 6x² + 12x + 6

= -3x² + 39x + 6

= -3( x² - 13x - 2 )

f) ( x + y )( x² - xy + y² ) + ( x - y )( x² + xy + y² ) - 2x³

= x³ + y³ + x³ - y³ - 2x³

= 0

g) x² + 2x( y + 1 ) + y² + 2y + 1

= x² + 2x( y + 1 ) + ( y² + 2y + 1 )

= x² + 2x( y + 1 ) + ( y + 1 )²

= ( x + y + 1 )²

= [ ( x + y ) + 1 ]²

= ( x + y )² + 2( x + y ) + 1

= x² + 2xy + y² + 2x + 2y + 1

\(a,x^2y-8x+xy-8=xy\left(x+1\right)-8\left(x+1\right)=\left(xy-8\right)\left(x+1\right)\\ b,=\left(x+3y\right)^2-9=\left(x+3y-3\right)\left(x+3y+3\right)\)

\(A=3x^2\left(2x^2-7x-2\right)-6x^2\left(x^2-4x-1\right)-3x^3+15\\ A=6x^4-21x^3-6x^2-6x^4+24x^3+6x^2-3x^3+15\\ A=15\left(đpcm\right)\)

\(Sửa:\left(6x^3-7x^2+2x\right):\left(2x+1\right)\\ =\left(6x^3+3x^2-10x^2-5x\right):\left(2x+1\right)\\ =\left[3x^2\left(2x+1\right)-5x\left(2x+1\right)\right]:\left(2x+1\right)\\ =3x^2-5x\)

Bạn thu gọn các đa thức rồi thay thế vào sẽ tính ra ngay nha!

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