Giải bài 1 trang 16 SGK Toán 8 tập 1 – Cánh diều

Đề bài

Thực hiện phép tính:

a) \(\left( { – xy} \right)\left( { – 2{{\rm{x}}^2}y + 3{\rm{x}}y – 7{\rm{x}}} \right)\)                               

b) \(\left( {\dfrac{1}{6}{x^2}{y^2}} \right)\left( { – 0,3{{\rm{x}}^2}y – 0,4{\rm{x}}y + 1} \right)\)

c) \(\left( {x + y} \right)\left( {{x^2} + 2{\rm{x}}y + {y^2}} \right)\)                                    

d) \(\left( {x – y} \right)\left( {{x^2} – 2{\rm{x}}y + {y^2}} \right)\)

Lời giải chi tiết

a)

\(\begin{array}{l}\left( { – xy} \right)\left( { – 2{{\rm{x}}^2}y + 3{\rm{x}}y – 7{\rm{x}}} \right)\\ = \left( { – xy} \right).\left( { – 2{{\rm{x}}^2}y} \right) + \left( { – xy} \right)\left( {3{\rm{x}}y} \right) + \left( { – xy} \right).\left( { – 7{\rm{x}}} \right)\\ = 2{{\rm{x}}^3}{y^2} – 3{{\rm{x}}^2}{y^2} + 7{{\rm{x}}^2}y\end{array}\)

b)

\(\begin{array}{l}\left( {\dfrac{1}{6}{x^2}{y^2}} \right)\left( { – 0,3{{\rm{x}}^2}y – 0,4{\rm{x}}y + 1} \right)\\ = \left( {\dfrac{1}{6}{x^2}{y^2}} \right).\left( { – 0,3{{\rm{x}}^2}y} \right) + \left( {\dfrac{1}{6}{x^2}{y^2}} \right).\left( { – 0,4{\rm{x}}y} \right) + \left( {\dfrac{1}{6}{x^2}{y^2}} \right).1\\ =  – \dfrac{1}{{20}}{x^4}{y^3} – \dfrac{1}{{15}}{x^3}{y^3} + \dfrac{1}{6}{x^2}{y^2}\end{array}\)

c)

\(\begin{array}{l}\left( {x + y} \right)\left( {{x^2} + 2{\rm{x}}y + {y^2}} \right)\\ = x.{x^2} + x.2{\rm{x}}y + x.{y^2} + y.{x^2} + y.2{\rm{x}}y + y.{y^2}\\ = {x^3} + 2{{\rm{x}}^2}y + x{y^2} + {x^2}y + 2{\rm{x}}{y^2} + {y^3}\\ = {x^3} + 3{{\rm{x}}^2}y + 3{\rm{x}}{y^2} + {y^3}\end{array}\)

d)

\(\begin{array}{l}\left( {x – y} \right)\left( {{x^2} – 2{\rm{x}}y + {y^2}} \right)\\ = x.{x^2} + x.\left( { – 2{\rm{x}}y} \right) + x.{y^2} + \left( { – y} \right).{x^2} + \left( { – y} \right).\left( { – 2{\rm{x}}y} \right) + \left( { – y} \right).{y^2}\\ = {x^3} – 2{{\rm{x}}^2}y + x{y^2} – {x^2}y + 2{\rm{x}}{y^2} – {y^3}\\ = {x^3} – 3{{\rm{x}}^2}y + 3{\rm{x}}{y^2} – {y^3}\end{array}\)