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Giải bài 1.13 trang 14 SGK Toán 8 tập 1 - Kết nối tri thức

Cho đa thức P a) Thu gọn và tìm bậc của đa thức P; b) Tính giá trị của đa thức P tại x=-4;y=2 và z=1.

♕Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

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

Cho đa thức \(P = 8{x^2}{y^2}z - 2xyz + 5{y^2}z - 5{x^2}{y^2}z + {x^2}{y^2} - 3{x^2}{y^2}z.\) a)      Thu gọn và tìm bậc của đa thức P; b)      Tính giá trị của đa thức P tại x=-4;y=2 và z=1.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

a)      Sử dụng tính chất giao hoán, kết hợp các hạng tử đồng dạng với nhau rồi thu gọn. Bậc của đa thức là bậc của hạng tử có bậc cao nhất trong dạng thu gọn của đa thức đó. b)      Thay các giá trị x=-4;y=2 và z=1 vào đa thức P rồi tính giá trị.

Lời giải chi tiết

a)\(\begin{array}{l}P = 8{x^2}{y^2}z - 2xyz + 5{y^2}z - 5{x^2}{y^2}z + {x^2}{y^2} - 3{x^2}{y^2}z\\ = \left( {8{x^2}{y^2}z - 5{x^2}{y^2}z - 3{x^2}{y^2}z} \right) - 2xyz + 5{y^2}z + {x^2}{y^2}\\ =  - 2xyz + 5{y^2}z + {x^2}{y^2}\end{array}\)Hạng tử có bậc cao nhất là \({x^2}{y^2}\) có bậc là 2 + 2 = 4 nên bậc của đa thức là 4.b) Thay \(x =  - 4;y = 2;z = 1\) vào P ta được \(P =  - 2.\left( { - 4} \right).2.1 + {5.2^2}.1 + {\left( { - 4} \right)^2}{.2^2} = 16 + 20 + 64 = 100.\)

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