急~請問如何化簡？ (2x²+1)³-3(x²-2)³-(2x²-1)(4x⁴+2x²+1)?
回答 (2)
2020-08-31 8:50 pm
✔ 最佳答案
(2x^2+1)^3 - 3(x^2-2)^3 - (2x^2-1)(4x^4+2x^2+1)= (8x^6+12x^4+6x^2+1) - 3(x^2-2)^3 - (8x^6-1)
= 12x^4+6x^2 - 3(x^6-6x^4+12x^2-8)
= -3(x^6-10x^4+10x^2-8)
2020-08-31 8:52 pm
恆等式：
(a ± b)³ = a³ ± 3a²b + 3ab² ± b³
(2x² + 1)³ - 3(x² - 2)³ - (2x² - 1)(4x⁴ + 2x² + 1)
= (2x²)³ + 3(2x²)²(1) + 3(2x²)(1)² + (1)³
- 3[(x²)³ - 3(x)²(2) + 3(x²)(2)² - (2)³]
- (8x⁶ + 4x⁴ + 2x² - 4x⁴ - 2x² - 1)
= 8x⁶ + 12x⁴ + 6x² + 1
-3x⁶ + 18x⁴ - 36x² + 24
-8x⁶ + 0x⁴ + 0x² + 1
= -3x⁶ + 30x⁴ - 30x² + 26
(a ± b)³ = a³ ± 3a²b + 3ab² ± b³
(2x² + 1)³ - 3(x² - 2)³ - (2x² - 1)(4x⁴ + 2x² + 1)
= (2x²)³ + 3(2x²)²(1) + 3(2x²)(1)² + (1)³
- 3[(x²)³ - 3(x)²(2) + 3(x²)(2)² - (2)³]
- (8x⁶ + 4x⁴ + 2x² - 4x⁴ - 2x² - 1)
= 8x⁶ + 12x⁴ + 6x² + 1
-3x⁶ + 18x⁴ - 36x² + 24
-8x⁶ + 0x⁴ + 0x² + 1
= -3x⁶ + 30x⁴ - 30x² + 26
收錄日期: 2021-05-04 02:31:03
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20200831121645AASPM8N