题目

1,(-a+b^2)(-a-b^2）
2,(-1/2x+3y)(-3y-1/2x)
3,(a^2+5ab)(5ab-a^2)
4,(a^n+b)(b-a^n)
5,(a+1)(a-1)(1+a^2)
6,1225-75^2
7,51*49
8,(-1001)*(-999)
9,(2x-3)(-2x-3)-x(x-1)
10,(a-b+c)(a+b-c)
11,(x+y)(x-y)(-x+y)(-x-y)
12,(2m+n)^2
13,(-2m+n)^2
14,(-1/3x-3y)^2
15,(a+b)^2-(a-b)^2
16,(2x+y)^2+(y-2x)^2
17,999^2
18,(x+y)(x-y)(x^2-y^2)
(x^2-2y)^2-(x^2+2y)^2
最后一题是19，

提问时间：2020-12-27

答案

1. = (-a)² - (b²)² = a² - b⁴
2. = (-x/2)² - (3y)² = x²/4 - 9y²
3. = (5ab)² - (a²)² = 25a²b² - a⁴ = a²(25b² - a²)
4. = b² - (aⁿ)² = b² - a²ⁿ
5. = (a² - )(a² + 1) = a⁴ - 1
6. = 35² - 75² = (35 + 75)(35 - 75) = 110*(-40) = -4400
7. = (50 + 1)(50 - 1) =50² - 1² = 2500 - 1 = 2499
8. = 1001*999 = (1000 + 1)(1000 - 1) = 1000² - 1 = 1000000 - 1 = 999999
9. = (-3)² - (2x)² - x² + 1 = 9 - 4x² - x² + 1 = 10 - 5x²
10. = [a - (b - c)][a + (b - c)] = a² - (b - c)² = a² - b² + 2bc - c²
11. = (x² - y²)[(-x)² - y²] = (x² - y²)² = x⁴ - 2x²y² + y⁴
12. = 4m² + 4mn + n²
13. = 4m² - 4mn + n²
14. = (x/3 + 3y)² = x²/9 + 2xy + 9y²
15. = [(a + b) + (a - b)][(a + b) - (a - b)] = 2a*2b = 4ab
16. = 4x² + 4xy + y² + y² - 4xy + 4x² = 8x² + 2y²
17. = (1000 - 1)² = 1000000 - 2000 + 1 = 998001
18. = (x² - y²)(x² - y²) = x⁴ - 2x²y² + y⁴
19. = (x² - 2y + x² + 2y)(x² - 2y - x² - 2y) = 2x²(-4y)= -8x²y