Toán Lớp 8: Giải hộ mình vớiiiii
a, x^2y+xy^2-x-y
b, ax^2-ay^2-7x-7y
c, ax^2+ay-bx^2-by
d, x(x+1)^2+x(x-5)-5(x+1)^2
e, ab(a-b)+bc(b-c)+ca(c-a)
g, (a+b+c)^3-a^3-b^3-c^3
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Toán Lớp 8: Giải hộ mình vớiiiii
a, x^2y+xy^2-x-y
b, ax^2-ay^2-7x-7y
c, ax^2+ay-bx^2-by
d, x(x+1)^2+x(x-5)-5(x+1)^2
e, ab(a-b)+bc(b-c)+ca(c-a)
g, (a+b+c)^3-a^3-b^3-c^3
Comments ( 1 )
a){x^2}y + x{y^2} – x – y\\
= xy\left( {x + y} \right) – \left( {x + y} \right)\\
= \left( {x + y} \right)\left( {xy – 1} \right)\\
b)a.{x^2} – a.{y^2} – 7x – 7y\\
= a.\left( {{x^2} – {y^2}} \right) – 7.\left( {x + y} \right)\\
= \left( {x + y} \right).\left( {a.\left( {x – y} \right) – 7} \right)\\
= \left( {x + y} \right)\left( {a.x – a.y – 7} \right)\\
c)a.{x^2} + a.y – b{x^2} – by\\
= {x^2}\left( {a – b} \right) + y\left( {a – b} \right)\\
= \left( {a – b} \right)\left( {{x^2} + y} \right)\\
d)x{\left( {x + 1} \right)^2} + x\left( {x – 5} \right) – 5{\left( {x + 1} \right)^2}\\
= {\left( {x + 1} \right)^2}\left( {x – 5} \right) + x\left( {x – 5} \right)\\
= \left( {x – 5} \right)\left( {{x^2} + 2x + 1 + x} \right)\\
= \left( {x – 5} \right)\left( {{x^2} + 3x + 1} \right)\\
e)ab\left( {a – b} \right) + bc\left( {b – c} \right) + ca\left( {c – a} \right)\\
= {a^2}b – a{b^2} + {b^2}c – b{c^2} + ca\left( {c – a} \right)\\
= b.\left( {{a^2} – {c^2}} \right) – {b^2}\left( {a – c} \right) – ca\left( {a – c} \right)\\
= \left( {a – c} \right)\left( {b\left( {a + c} \right) – {b^2} – ca} \right)\\
= \left( {a – c} \right)\left( {ba + bc – {b^2} – ca} \right)\\
= \left( {a – c} \right)\left( {a – b} \right).\left( {b – c} \right)\\
g){\left( {a + b + c} \right)^3} – {a^3} – {b^3} – {c^3}\\
= \left( {a + b + c – a} \right)\left[ {{{\left( {a + b + c} \right)}^2} + \left( {a + b + c} \right).a + {a^2}} \right]\\
– \left( {b + c} \right)\left( {{b^2} – bc + {c^2}} \right)\\
= \left( {b + c} \right).\left( \begin{array}{l}
{a^2} + {b^2} + {c^2} + 2ab + 2bc + 2ac + {a^2} + ab + ac + {a^2}\\
– {b^2} + bc – {c^2}
\end{array} \right)\\
= \left( {b + c} \right)\left( {3{a^2} + 3ab + 3ac + 3bc} \right)
\end{array}$