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Khái niệm đơn thức và đơn thức thu gọn

Đơn thức là gì? Đơn thức thu gọn là gì?
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1. Lý thuyết

- Khái niệm:

+ Đơn thức꧂ là biểu thức đại số chỉ gồm một số hoặc một biến, hoặc có dạng tích của những số và biến.

+ Đơn thức thu gọnꦰ là đơn thức chỉ gồm một số, hoặc có dạng tích của một số với những biến, mỗi biến chỉ xuất hiện một lần và đã được nâng lên lũy thừa với số mũ nguyên dương.

+ Trong một đơn thức thu gọn, phần số còn gọi là hệ số, phần còn lại gọi là phần biến.

+ Bậc của đơn thức là tổng số mũ💛 của các biến trong một đơn thức thu gọn với hệ số khác 0.

- Chú ý:

+ Số thực khác 0 là đơn thức bậc không.+ Số 0 được gọi là đơn thức không có bậc.

- Cách thu gọn các đơn thức:

Với các đơn thức chưa là đơn thức thu gọn, ta có thể thu gọn chúng bằng cách áp dụng các tính chất của phép nhân và phép nâng lên lũy thừa.

2. Ví dụ minh họa

- Đơn thức: \(1;2xy; - \frac{3}{4}{x^2}y( - 4x);...\)

- Đơn thức thu gọn: \(1;2xy;5{x^2}{y^4}z;...\)

\(3{x^2}yx\) không phải đơn thức thu gọn vì biến x xuất hiện 2 lần.

\( - \frac{3}{4}{x^2}yz( - 4y){z^2}\) không phải🦂 đơn thức thu gọn vì biến y và biến z xuất hiện 2 lần.

- Thu gọn đơn thức \( - \frac{3}{4}{x^2}yz( - 4y){z^2}\) như sau:

\(\begin{array}{l} - \frac{3}{4}{x^2}yz( - 4y){z^2}\\ = \left( { - \frac{3}{4}} \right).( - 4).{x^2}.(y.y).\left( {z.{z^2}} \right)\\ = 3{x^2}{y^2}{z^3}\end{array}\)

- Đơn thức \(3{x^2}{y^2}{z^3}\) có hệ số là 3, phần biến là \({x^2}{y^2}{z^3}\),  bậc là 2 + 2 + 3 = 7

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