數學 簡易多項式(展開)

2007-07-17 5:28 pm
(展開)1.(3a+1)(a-2)
(展開)2.(3b(2次方)-2b+1)(b-1)
(展開)3.(2x(2次方)-3x+1)(x(2次方)--x-1)

回答 (2)

2007-07-17 5:52 pm
✔ 最佳答案
1. (3a + 1) (a - 2)
= 3a^2 - 3a + a - 2
= 3a^2 - 2a - 2

2. (3b^2 - 2b + 1) (b - 1)
= 3b^3 - 3b - 2b^2 + 2b + b - 1
= 3b^3 - 2b^2 -1

3. (2x^2 - 3x + 1) (x^2 - x - 1)
= 2x^4 - 2x^3 - 2x^2 - 3x^3 + 3x^2 + 3x + x^2 - x - 1
= 2x^4 - 5x^3 + 2x^2 + 2x - 1
2007-07-17 6:30 pm
1)
(3a+1)(a-2)
= a(3a+1) - 2(3a+1)
= 3a^2 + a - 6a - 2
= 3a^2 -5a -2

2)
(3b^2-2b+1)(b-1)
= b(3b^2-2b+1) - (3b^2-2b+1)
= 3b^3 - 2b^2 + b - 3b^2 + 2b - 1
= 3b^3 - 5b^2 + 3b - 1

3)
(2x^2-3x+1)(x^2-x-1) <-- 題目應該係咁, right? 應該唔係減 (-x) 吧~
= x^2(2x^2-3x+1) - x(2x^2-3x+1) - (2x^2-3x+1)
= (2x^4 - 3x^3 + x^2) - (2x^3 - 3x^2 + x) - (2x^2 - 3x + 1)
= 2x^4 - 3x^3 + x^2 - 2x^3 + 3x^2 - x - 2x^2 + 3x - 1
= 2x^4 - 3x^3 - 2x^3 + x^2 + 3x^2 - 2x^2 - x + 3x - 1 (調下位, 易睇 d)
= 2x^4 - 5x^3 + 2x^2 + 2x -1


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