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Giải mục 1 trang 19, 20 SGK Toán 8 tập 1 - Kết nối tri thức

Luyện tập 1 trang 19 Nhân hai đơn thức:

♏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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Luyện tập 1

Video hướng dẫn giải

Nhân hai đơn thức: a)      \(3{x^2}\) và \(2{x^3}\) b)      \( - xy\) và \(4{z^3}\) c)      \(6x{y^3}\) và \( - 0,5{x^2}\)

Phương pháp giải:

Nối hai đơn thức với nhau bởi dấu nhân rồi bỏ dấu ngoặc (nếu có) và thu gọn đơn thức nhận được.

Lời giải chi tiết:

a)      \(3{x^2}.2{x^3} = \left( {3.2} \right).\left( {{x^2}.{x^3}} \right) = 6{x^5}\) b)      \(\left( { - xy} \right).4{z^3} =  - 4xy{z^3}\) c)      \(6x{y^3}.\left( { - 0,5{x^2}} \right) = \left[ {6.\left( { - 0.5} \right)} \right].\left( {x.{x^2}} \right).{y^3} =  - 3{x^3}y^3\)

HĐ1

Video hướng dẫn giải

Hãy nhớ lại quy tắc nhân đơn thức với đa thức trong trường hợp chúng có một biến bằng cách thực hiện phép nhân \(\left( {5{x^2}} \right).\left( {3{x^2} - x - 4} \right)\)

Phương pháp giải:

Nhân đơn thức với từng hạng tử của đa thức rồi cộng các tích với nhau.

Lời giải chi tiết:

\(\begin{array}{l}\left( {5{x^2}} \right).\left( {3{x^2} - x - 4} \right)\\ = 5{x^2}.3{x^2} - 5{x^2}.x - 5{x^2}.4\\ = 15{x^4} - 5{x^3} - 20{x^2}\end{array}\)

HĐ2

Video hướng dẫn giải

Bằng cách tương tự, hãy làm phép nhân \(\left( {5{x^2}y} \right).\left( {3{x^2}y - xy - 4y} \right)\).

Phương pháp giải:

Nhân đơn thức với từng hạng tử của đa thức rồi cộng các tích với nhau.

Lời giải chi tiết:

\(\begin{array}{l}\left( {5{x^2}y} \right).\left( {3{x^2}y - xy - 4y} \right)\\ = 5{x^2}y.3{x^2}y - 5{x^2}y.xy - 5{x^2}y.4y\\ = 15{x^4}{y^2} - 5{x^3}{y^2} - 20{x^2}{y^2}\end{array}\)

Luyện tập 2

Video hướng dẫn giải

Làm tính nhân: a)      \(\left( {xy} \right).\left( {{x^2} + xy - {y^2}} \right)\); b)      \(\left( {xy + yz + zx} \right).\left( { - xyz} \right)\).

Phương pháp giải:

Nhân đơn thức với từng hạng tử của đa thức rồi cộng các tích với nhau.

Lời giải chi tiết:

a) \(\begin{array}{l}\left( {xy} \right).\left( {{x^2} + xy - {y^2}} \right)\\ = xy.{x^2} + xy.xy - xy.{y^2}\\ = {x^3}y + {x^2}{y^2} - x{y^3}\end{array}\) b) \(\begin{array}{l}\left( {xy + yz + zx} \right).\left( { - xyz} \right)\\ = xy.\left( { - xyz} \right) + yz.\left( { - xyz} \right) + zx.\left( { - xyz} \right)\\ =  - {x^2}{y^2}z - x{y^2}{z^2} - {x^2}y{z^2}\end{array}\)

Vận dụng

Video hướng dẫn giải

Rút gọn biểu thức: \({x^3}\left( {x + y} \right) - x\left( {{x^3} + {y^3}} \right)\).

Phương pháp giải:

Muốn nhân đơn thức với đa thức, ta nhân đơn thức với từng hạng tử của đa thức rồi cộng các tích với nhau. Sau đó, nhóm các hạng tử đồng dạng để thu gọn đa thức.

Lời giải chi tiết:

\(\begin{array}{l}{x^3}\left( {x + y} \right) - x\left( {{x^3} + {y^3}} \right)\\ = {x^3}.x + {x^3}.y - \left( {x.{x^3} + x.{y^3}} \right)\\ = {x^4} + {x^3}y - {x^4} - x{y^3}\\ = \left( {{x^4} - {x^4}} \right) + {x^3}y - x{y^3}\\ = {x^3}y - x{y^3}\end{array}\)

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