Bai 3: Thu gon ve hang dang thuc: 1) (2x+1)2+2(2x+1)+1 2) (3x-2y)2 +4(3x-2y) +4 3) (x+3)2+(x-2)2-2(x+3)(x-2) 4) (3x-5)2-2(3x-5)(3x+5)+(3x+5) 5) (x-y)2+(x+y)2-2(x+y)(x-y) 6) (5-x)+(x+5)2-(2x+10)(x-5)  Hellppp giúp mik vs

1) (2x+1)² + 2(2x+1) + 1
= (2x+1)² + 2(2x+1) + 1
= (2x+1)² + 2(2x+1) + 1
= (2x + 1)(2x + 1) + 4x + 2 + 1.
Giải chi tiết, ta có:
= 4x² + 4x + 1 + 4x + 2 + 1
= 4x² + 8x + 4
= 4(x² + 2x + 1)
= 4(x+1)².

2) (3x-2y)² + 4(3x-2y) + 4
= (3x-2y)² + 4(3x-2y) + 4
= (3x-2y)(3x-2y) + 12x - 8y + 4
= 9x² - 12xy + 4y² + 12x - 8y + 4
= 9x² + (12x - 12xy) + (4y² - 8y + 4)
= 9x² + 12x - 12xy + 4y² - 8y + 4 cũng là phương trình bậc 2 ở dạng chuẩn.


3) (x+3)² + (x-2)² - 2(x+3)(x-2)
= (x² + 6x + 9) + (x² - 4x + 4) - 2[(x² + x - 6)]
= x² + 6x + 9 + x² - 4x + 4 - 2(x² - x - 6)
= 2x² + 2x + 13 - 2(x² - x - 6)
= 2x² + 2x + 13 - 2x² + 2x + 12
= 4x + 25.


4) (3x-5)² - 2(3x-5)(3x+5) + (3x+5)
= (3x-5)(3x-5) - 2[(3x² - 25)] + (3x + 5)
= 9x² - 30x + 25 - 2(3x² - 25) + 3x + 5
= 9x² - 30x + 25 - 6x² + 50 + 3x + 5
= (9x² - 6x²) + (-30x + 3x) + (25 + 50 + 5)
= 3x² - 27x + 80.


5) (x-y)² + (x+y)² - 2(x+y)(x-y)
= (x² - 2xy + y²) + (x² + 2xy + y²) - 2[(x² - y²)]
= 2x² + 2y² - 2(x² - y²)
= 2x² + 2y² - 2x² + 2y²
= 4y².


6) (5-x) + (x+5)² - (2x+10)(x-5)
= (5 - x) + (x² + 10x + 25) - [2x² - 10]
= 5 - x + x² + 10x + 25 - 2x² + 20
= -x² + 9x + 50.