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Giải bài 4 trang 8 sách bài tập toán 8 - Cánh diều

Thu gọn mỗi đa thức sau:

꧟Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Cánh diều

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

Thu gọn mỗi đa thức sau: a) \({x^2}{y^5} + 2x{y^2} - {x^2}{y^5} + \frac{{24}}{{35}}x{y^2}\) b) \( - 11{y^2}{z^3} - 22x{y^3}{z^3} + 2{y^2}{z^3} - 33x{y^3}{z^3} - 72\) c) \(\frac{{\sqrt 4 }}{{41}}{x^2}{y^4}{z^3} + {x^2}{y^4}z + \frac{{39}}{{41}}{x^2}{y^4}{z^3} - {x^2}{y^4}z + {z^{18}}\)

Phương pháp giải - Xem chi tiết

Thu gọn đa thức là làm cho đa thức không còn hai đơn thức nào đồng dạng.

Lời giải chi tiết

a) Ta có: \({x^2}{y^5} + 2x{y^2} - {x^2}{y^5} + \frac{{24}}{{35}}x{y^2} = \left( {{x^2}{y^5} - {x^2}{y^5}} \right) + \left( {2x{y^2} + \frac{{24}}{{35}}x{y^2}} \right) = \frac{{94}}{{35}}x{y^2}\) b) Ta có: \(\begin{array}{l} - 11{y^2}{z^3} - 22x{y^3}{z^3} + 2{y^2}{z^3} - 33x{y^3}{z^3} - 72\\ = \left( { - 11{y^2}{z^3} + 2{y^2}{z^3}} \right) + \left( { - 22x{y^3}{z^3} - 33x{y^3}{z^3}} \right) - 72\\ =  - 9{y^2}{z^3} - 55x{y^3}{z^3} - 72\end{array}\) c) Ta có: \(\begin{array}{l}\frac{{\sqrt 4 }}{{41}}{x^2}{y^4}{z^3} + {x^2}{y^4}z + \frac{{39}}{{41}}{x^2}{y^4}{z^3} - {x^2}{y^4}z + {z^{18}}\\ = \left( {\frac{{\sqrt 4 }}{{41}}{x^2}{y^4}{z^3} + \frac{{39}}{{41}}{x^2}{y^4}{z^3}} \right) + \left( {{x^2}{y^4}z - {x^2}{y^4}z} \right) + {z^{18}}\\ = {x^2}{y^4}{z^3} + {z^{18}}\end{array}\)

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