Toán Lớp 8: phân tich đa thức thành nhân tử:
a)x^4+x^3+4x^2+2x+4
b) (2ab-2cd)^2-(a^2+b^2-c^2-d^2)^2
c) 3x(2x-3y)+(3y-2x)^2-(5x+2y^(5x-2y)
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Toán Lớp 8: phân tich đa thức thành nhân tử:
a)x^4+x^3+4x^2+2x+4
b) (2ab-2cd)^2-(a^2+b^2-c^2-d^2)^2
c) 3x(2x-3y)+(3y-2x)^2-(5x+2y^(5x-2y)
Comments ( 1 )
a){x^4} + {x^3} + 4{x^2} + 2x + 4\\
= {x^4} + {x^3} + 2{x^2} + 2{x^2} + 2x + 4\\
= {x^2}\left( {{x^2} + x + 2} \right) + 2\left( {{x^2} + x + 2} \right)\\
= \left( {{x^2} + x + 2} \right)\left( {{x^2} + 2} \right)\\
b){\left( {2ab – 2cd} \right)^2} – {\left( {{a^2} + {b^2} – {c^2} – {d^2}} \right)^2}\\
= \left( {2ab – 2cd – {a^2} – {b^2} + {c^2} + {d^2}} \right).\\
\left( {2ab – 2cd + {a^2} + {b^2} – {c^2} – {d^2}} \right)\\
= \left[ {{{\left( {c – d} \right)}^2} – {{\left( {a – b} \right)}^2}} \right].\left[ {{{\left( {a + b} \right)}^2} – {{\left( {c + d} \right)}^2}} \right]\\
= \left( {c – d – a + b} \right)\left( {c – d + a – b} \right).\left( {a + b + c + d} \right)\left( {a + b – c – d} \right)
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