Question

分解因式： -(2n+1)^2+25 9(a+b)^2-4(a-b)^2 16(a-b)^2-25(a+b)^2 a^5-a^3 2分之1-8分之1x^2

(x-1)+b^2(1-x) -16+x^4y^4 3a-3ay^4 4x^2-12x+9

Answer 1

-(2n + 1)² + 25 = 5² - (2n + 1)² = (6 + 2n)(4 - 2n) = 4(3 + n)(2 - n)
9(a + b)² - 4(a - b)² = [3(a + b)]² - [2(a - b)]² = (5a + b)(a + 5b)
16(a - b)² - 25(a + b)² = [4(a - b)]² - [5(a + b)]² = - (9a + b)(a + 9b)
a^5-a³ = a³(1 - a²) = a³(1 + a)(1 - a)
1/2 - x²/8 = (2 + x)(2 - x) / 8
(x - 1) + b²(1 - x) = (x - 1)(1 - b²) = (x - 1)(1 + b)(1 - b)
-16 + x⁴y⁴ = [(xy)²]² - 4² = [(xy)² + 4][(xy)² - 4] =(x²y² + 4)(xy + 2)(xy - 2)
3a - 3ay⁴= 3a(1 - y) = 3a(1 + y²)(1 + y)(1 - y)
4x² - 12x + 9 = (2x - 3)²