Rút gọn:
a) ( x+1) (x+3) – (x-1) (x-3) + 2x (1-x)
b) (3x +1) (x+1) – (x+3) (3x – 2)
Phân tích đa thức thành nhân tử :
a) x^2 + 4y^2 – 4xy – 9
b) x^3 – 1/16x
c) x^3 + 4x^2 – 8x – 8
d) x^3 + 6x^2 + 9x – xy^2
Rút gọn:
a) ( x+1) (x+3) – (x-1) (x-3) + 2x (1-x)
b) (3x +1) (x+1) – (x+3) (3x – 2)
Phân tích đa thức thành nhân tử :
a) x^2 + 4y^2 – 4xy – 9
b) x^3 – 1/16x
c) x^3 + 4x^2 – 8x – 8
d) x^3 + 6x^2 + 9x – xy^2
\(\begin{array}{l}
a){\rm{ }}\left( {{\rm{ }}x + 1} \right)\left( {x + 3} \right) – \left( {x – 1} \right)\left( {x – 3} \right) + {\rm{ }}2x\left( {1 – x} \right)\\
= {x^2} + 3x + x + 3 – \left( {{x^2} – 3x – x + 3} \right) + 2x – 2{x^2}\\
= {x^2} + 4x + 3 – {x^2} + 3x + x – 3 + 2x – 2{x^2}\\
= – 2{x^2} + 10x\\
b){\rm{ }}\left( {3x{\rm{ }} + 1} \right)\left( {x + 1} \right){\rm{ }} – {\rm{ }}\left( {x + 3} \right)\left( {3x – 2} \right)\\
= 3{x^2} + 3x + x + 1 – \left( {3{x^2} – 2x + 9x – 6} \right)\\
= 3{x^2} + 4x + 1 – 3{x^2} + 2x – 9x + 6\\
= – 3x + 7
\end{array}\)