a)

\(2x\left(9-x\right)+\left(2x+5\right)\left(x+1\right)\\ =18x-2x^2+2x^2+5x+2x+5\\ =25x+5\\ =5\left(5x+1\right)\)

b)

\(\left(x-3\right)^2+\left(x+3\right)^2+2\left(3-x\right)\left(3+x\right)\\ =\left(3-x\right)^2+2\left(3-x\right)\left(3+x\right)+\left(3+x\right)^2\\ =\left[\left(3-x\right)+\left(3+x\right)\right]^2\\ =6^2=36\)

`Answer:`

`a)`

`A=5(x+1)^2-3(x-3)^2-4(x^2-4)`

`=>A=5(x^2+2x+1)-3(x^2-6x+9)-4x^2+16`

`=>A=5x^2+10x+5-3x^2+18x-27-4x^2+16`

`=>A=(5x^2-3x^2-4x^2)+(10x+18x)+(5-27+16)`

`=>A=-2x^2+28x-6`

`b)`

`B=5(x+1)^2-3(x-3)^2-4(x+2)(x-2)`

`=2x(3x+5)-3(3x+5)-2x(x^2-4x+4)-[(2x)^2-3^2]`

`=6x^2+10x-9x-15-2x^3+8x^2-8x-4x^2+9`

`=(6x^2-4x^2+8x^2)-2x^3+(10x-9x-8x)+(-15+9)`

Thay `x=-7` vào ta được:

`B=10(-7)^2-2(-7)^3-7(-7)-6`

`=>B=10.49-2(-343)+49-6`

`=>B=490+686+49-6`

`=>B=1219`

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

\(D=\left(4x^2+4x+1\right)-\left(4x^2-12x+9\right)+6x\)

\(D=\left(4x^2-4x^2\right)+\left(4x-12x+6x\right)+\left(1-9\right)\)

\(D=-2x-8\)

_______________________

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

\(E=\left(x^2-8x+16\right)-\left(x^2+2x\right)-2x+3\)

\(E=\left(x^2-x^2\right)-\left(8x+2x+2x\right)+\left(16+3\right)\)

\(E=-12x+19\)

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

\(D=\left[\left(2x\right)^2+2.2x.1+1^2\right]-\left[\left(2x\right)^2-2.2x.3+3^2\right]+6x\)

\(D=4x^2+4x+1-\left(4x^2-12x+9\right)+6x\)

\(D=4x^2+4x+1-4x^2+12x-9+6x\)

\(D=22x-8\)

___________

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

\(E=\left(x^2-2.x.4+4^2\right)-\left(x^2+2x\right)-2x+3\)

\(E=x^2-8x+16-x^2-2x-2x+3\)

\(E=-12x+19\)

a) Rút gọn biểu thức D = (2x + 1)2 - (2x - 3)2 + 6x:

Bắt đầu bằng việc mở ngoặc:
D = (4x^2 + 4x + 1) - (4x^2 - 12x + 9) + 6x

Tiếp theo, kết hợp các thành phần tương tự:
D = 4x^2 + 4x + 1 - 4x^2 + 12x - 9 + 6x

Tiếp tục đơn giản hóa:
D = 4x^2 - 4x^2 + 4x + 12x + 6x + 1 - 9

Kết quả cuối cùng:
D = 22x - 8

b) Rút gọn biểu thức E = (x - 4)2 - x(x + 2) - 2x + 3:

Bắt đầu bằng việc mở ngoặc:
E = (x^2 - 8x + 16) - (x^2 + 2x) - 2x + 3

Tiếp theo, kết hợp các thành phần tương tự:
E = x^2 - 8x + 16 - x^2 - 2x - 2x + 3

Tiếp tục đơn giản hóa:
E = x^2 - x^2 - 8x - 2x - 2x + 16 + 3

Kết quả cuối cùng:
E = -12x + 19

Ta có: \(2x\left(3x-1\right)-\left(2x+1\right)\left(x-3\right)\)

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

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

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

Ta có: \(3\left(x^2-2x\right)-\left(4x+2\right)\left(x-1\right)\)

\(=3x^2-6x-\left(4x^2-4x+2x-2\right)\)

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

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

\(2x\left(3x-1\right)-\left(2x+1\right)\left(x-3\right)=6x^2-2x-2x^2+5x+3=4x^2+3x+3\)

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

cậu xem câu hỏi của Quỳnh Phạm nha

1) `2x(3x-1)-(2x+1)(x-3)`

`=6x^2-2x-2x^2+6x-x+3`

`=4x^2+3x+3`

2) `3(x^2-3x)-(4x+2)(x-1)`

`=3x^2-9x-4x^2+4x-2x+2`

`=-x^2-7x+2`

3) `3x(x-5)-(x-2)^2-(2x+3)(2x-3)`

`=3x^2-15x-(x^2-4x+4)-(4x^2-9)`

`=3x^2-15x-x^2+4x-4-4x^2+9`

`=-2x^2-11x+5`

4) `(2x-3)^2+(2x-1)(x+4)`

`=4x^2-12x+9+2x^2+8x-x-4`

`=6x^2-5x+5`

\(\left(x-2\right)^3+\left(2x+1\right)^2+2\left(x+2\right)\left(1-x\right)-9x^3+2x\)

\(=x^3-6x^2+12x-8+8x^3+12x^2+6x+1+2\left(x+2\right)\left(1-x\right)-9x^3+2x\)

\(=9x^3+6x^2+18x-7+2\left(x-x^2+2-2x\right)-9x^3+2x\)

\(=6x^2+20x-7-2x^2-2x+4=4x^2+18x-3\)

Trả lời:

( x - 2 )³ + ( 2x + 1 )³ + 2 ( x + 2 )( 1 - x ) - 9x³ + 2x

= x³ - 6x² + 12x - 8 + 8x³ + 12x² + 6x + 1 + 2 ( x - x² + 2 - 2x ) - 9x³ + 2x 

= 9x³ + 6x² + 18x - 7 + 2x - 2x² + 4 - 4x - 9x³ + 2x 

= 4x² + 18x - 3 

\(\left(2x-1\right)\left(x+2\right)-\left(x-3\right)\left(x+3\right)\)

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

\(=x^2+3x+7\)

\(\left(2x-1\right)\left(x+2\right)-\left(x-3\right)\left(x+3\right)\)

\(=2x^2+4x-x-2-x^2+9\)

\(=x^2+3x+7\)

\(2x^2+4x-x-2-x^2+9=x^2+3x+7\)

\(a,=x^2-6x+9-x^2+6x=9\\ b,=4x^2+4x+1-4x^2+9-4x-8=2\\ c,=\left(2x^2-2x-x+1\right):\left(x-1\right)\\ =\left(x-1\right)\left(2x-1\right):\left(x-1\right)=2x-1\)

`a)(x-3)^2-x(x-6)`

`=x^2-6x+9-x^2+6x=9`

`b)(2x+1)^2-(3+2x)(2x-3)-4(x+2)`

`=4x^2+4x+1-(4x^2-9)-4x-8`

`=2`

`c)(2x^2-3x+1):(x-1)`

`=(2x^2-2x-x+1):(x-1)`

`=[2x(x-1)-(x-1)]:(x-1)`

`=2x-1`

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

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

c) \(\left(2x^2-3x+1\right):\left(x-1\right)=\left[2x\left(x-1\right)-\left(x-1\right)\right]:\left(x-1\right)=\left[\left(x-1\right)\left(2x-1\right)\right]:\left(x-1\right)=2x-1\)

a) Ta có: \(\left(x+1\right)\left(x^2-x+1\right)-\left(x-1\right)\left(x^2+x+1\right)\)

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

=2

b) Ta có: \(\left(2x+3\right)\left(2x-3\right)-\left(2x+1\right)^2\)

\(=4x^2-9-4x^2-4x-1\)

\(=-4x-10\)