恆等式及因式分解 - Ans.fyi 參考答案

恆等式及因式分解

2012-10-13 5:20 am

1. 8x^4y^3-9x^4y^4

2. 12n^2m^6-8m^5n^2

3. 48x^2y^6-54y^3z^6

4. -30s^3u^4+24tu^5

5. ab^2-3ab+2a^2b

6. 14r^3s-7s+28s^2

7. 4p^4q-8p^3q+16p^3q^2

8. 81hk^2+9k^2h^2-27h^3k^3

9. 5x(x+y)-(x+y)

10. 12(3p+5)-5q(3p+5)

11. -m(n-8)+3n(n-8)

12. 9w(2w+1)+4(2w+1)

13. (a+b)^2+(a+b)b

14. 6s^2-2s(s+t)

回答 (1)

胡雪8°

2012-10-13 10:18 am

✔ 最佳答案

1.
8x⁴y³ - 9x⁴y⁴
= x⁴y³(8y - 9)

2.
12n²m⁶ - 8m⁵n²
= 12m⁶ n² - 8m⁵n²
= 4m⁵n²(3m - 8)

3.
48x²y⁶ - 54y³z⁶
= 2y³(24x²y³ - 27z⁶)

4.
-30s³u⁴ + 24tu⁵
= 24tu⁵ - 30s³u⁴
= 6u⁴(4tu - 5s³)

5.
ab² - 3ab + 2a²b
= ab(b - 3 + 2a)

6.
14r³s - 7s + 28s²
= 7s(2r² - 1 + 4s)

7.
4p⁴q - 8p³q + 16p³q²
= 4p³q(p - 2 + 4q)

8.
81hk² + 9k²h² - 27h³k³
= 81hk² + 9h²k² - 27h³k³
= 9hk²(9 + h - 3h²k)

9.
5x(x + y) - (x + y)
= (5x - 1)(x + y)

10.
12(3p + 5) - 5q(3p + 5)
= (12 - 5q)(3p + 5)

11.
-m(n - 8) + 3n(n - 8)
= 3n(n - 8) - m(n - 8)
= (3n - m)(n - 8)

12.
9w(2w + 1) + 4(2w + 1)
= (9w + 4)(2w + 1)

13.
(a + b)² + (a + b)b
= (a + b)[(a + b) + b]
= (a + b)(a + 2b)

14.
6s² - 2s(s + t)
= 6s² - 2s² - 2st
= 4s² - 2st
= 2s(2s - t)

參考: 胡雪

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