Bài 7: Thu gọn và sắp xếp theo lũy thừa giảm dần lũy thừa của biến
1) \( \mathcal{A}(x) = 6x^4 - 5x^2 + 4x - 3x^4 + 2x^3 \)
2) \( \mathcal{A}(x) = 3x^2 + 7x^3 - 3x^3 + 6x^3 - 3x^2 \)
3) \( \mathcal{A}(x) = x^5 + x^4 - 3x + 7 - 2x^4 - x^5 \)
4) \( \mathcal{A}(x) = 1 - 6x^7 + 5x^4 - 2 + 13x^5 - 8x^7 \)
5) \( \mathcal{A}(x) = 2 + 5x^2 - 3x^3 + 4x^2 - 2x - x^3 \)
6) \( \mathcal{A}(x) = -6x^4 + 2x^3 + x + 5x^4 - 2x + 3x^3 \)
1: \(A\left(x\right)=6x^4-5x^2+4x-3x^4+2x^3\)
\(=\left(6x^4-3x^4\right)+2x^3-5x^2+4x\)
\(=3x^4+2x^3-5x^2+4x\)
2: \(A\left(x\right)=3x^2+7x^3-3x^3+6x^3-3x^2\)
\(=\left(7x^3-3x^3+6x^3\right)+\left(3x^2-3x^2\right)\)
\(=10x^3\)
3: \(A\left(x\right)=x^5+x^4-3x+7-2x^4-x^5\)
\(=\left(x^5-x^5\right)+\left(x^4-2x^4\right)-3x+7\)
\(=-x^4-3x+7\)
4: \(A\left(x\right)=1-6x^7+5x^4-2+13x^5-8x^7\)
\(=\left(-6x^7-8x^7\right)+13x^5+5x^4+\left(1-2\right)\)
\(=-14x^7+13x^5+5x^4-1\)
5: \(A\left(x\right)=2+5x^2-3x^3+4x^2-2x-x^3\)
\(=\left(-3x^3-x^3\right)+\left(5x^2+4x^2\right)+\left(-2x\right)+2\)
\(=-4x^3+9x^2-2x+2\)
6: \(A\left(x\right)=-6x^4+2x^3+x+5x^4-2x+3x^3\)
\(=\left(-6x^4+5x^4\right)+\left(2x^3+3x^3\right)+\left(-2x+x\right)\)
\(=-x^4+5x^3-x\)
