Toán Lớp 8: Rút gọn biểu thức
a) A=(???? + 2)(x²− 2???? + 4) − ????(???? + 3)(???? − 3)
b) B=(2???? − 1)(4x²+ 2???? + 1) − 4????(2x² – 3)
c)???? = (???? − 1) ³ − (???? + 1) ³ + 6(???? + 1)(???? − 1)
d) ???? = (2???? − 1) ² (2???? − 3)(2???? + 1)
e)???? = (???? − 1) ³− 4????(???? − 1)(???? + 1) + 3(???? − 1)(???? ²+ ???? + 1)
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Comments ( 1 )
a)A = \left( {x + 2} \right)\left( {{x^2} – 2x + 4} \right) – x\left( {x + 3} \right)\left( {x – 3} \right)\\
= {x^3} + {2^3} – x\left( {{x^2} – 9} \right)\\
= {x^3} + 8 – {x^3} + 9x\\
= 9x + 8\\
b)\\
B = \left( {2x – 1} \right)\left( {4{x^2} + 2x + 1} \right) – 4x\left( {2{x^2} – 3} \right)\\
= 8{x^3} – 1 – 8{x^3} + 12x\\
= 12x – 1\\
c)\\
C = {\left( {x – 1} \right)^3} – {\left( {x + 1} \right)^3} + 6\left( {x + 1} \right)\left( {x – 1} \right)\\
= {x^3} – 3{x^2} + 3x – 1\\
– \left( {{x^3} + 3{x^2} + 3x + 1} \right)\\
+ 6\left( {{x^2} – 1} \right)\\
= – 6{x^2} – 2 + 6{x^2} – 6\\
= – 8\\
d)\\
D = {\left( {2x – 1} \right)^2} – \left( {2x – 3} \right)\left( {2x + 1} \right)\\
= 4{x^2} – 4x + 1 – \left( {4{x^2} – 4x – 3} \right)\\
= 4{x^2} – 4x + 1 – 4{x^2} + 4x + 3\\
= 4\\
e)\\
E = {\left( {x – 1} \right)^3} – 4x\left( {x – 1} \right)\left( {x + 1} \right) + 3\left( {x – 1} \right)\left( {{x^2} + x + 1} \right)\\
= {x^3} – 3{x^2} + 3x – 1\\
– 4x\left( {{x^2} – 1} \right) + 3\left( {{x^3} – 1} \right)\\
= {x^3} – 3{x^2} + 3x – 1 – 4{x^3} + 4x + 3{x^3} – 3\\
= – 3{x^2} + 7x – 4
\end{array}$