Question

Đã trả lời bởi chuyên gia

Answer 1

\[\begin{array}{l}
a){(2 - 3x)^2} - {(3 - x)^2}\\
= \left[ {\left( {2 - 3x} \right) - \left( {3 - x} \right)} \right].\left[ {\left( {2 - 3x} \right) + \left( {3 - x} \right)} \right]\\
= \left( {2 - 3x - 3 + x} \right)\left( {2 - 3x + 3 - x} \right)\\
= \left( { - 1 - 2x} \right)\left( {5 - 4x} \right)\\
b)49{(x - 3)^2} - 9{(x + 2)^2}\\
= {\left( {7x - 21} \right)^2} - {\left( {3x + 6} \right)^2}\\
= \left[ {\left( {7x - 21} \right) - \left( {3x + 6} \right)} \right].\left[ {\left( {7x - 21} \right) + \left( {3x + 6} \right)} \right]\\
= \left( {7x - 21 - 3x - 6} \right)\left( {7x - 21 + 3x + 6} \right)\\
= \left( {4x - 27} \right)\left( {10x - 15} \right)\\
c)2xy - {x^2} - {y^2} + 16\\
= 16 - \left( {{x^2} - 2xy + {y^2}} \right)\\
= {4^2} - {\left( {x - y} \right)^2}\\
= \left( {4 - x + y} \right)\left( {4 + x - y} \right)\\
d)2(x - 3) + 3({x^2} - 9)\\
= 2\left( {x - 3} \right) + 3\left( {x - 3} \right)\left( {x + 3} \right)\\
= \left( {x - 3} \right)\left( {2 + 3x + 9} \right)\\
= \left( {x - 3} \right)\left( {3x + 11} \right)\\
e)16{x^2} - {({x^2} + 4)^2}\\
= {\left( {4x} \right)^2} - {\left( {{x^2} + 4} \right)^2}\\
= \left( {4x - {x^2} - 4} \right)\left( {4x + {x^2} + 4} \right)\\
= - {\left( {x - 2} \right)^2}{\left( {x + 2} \right)^2}\\
f)1 - 2x + 2yz + {x^2} - {y^2} - {z^2}\\
= \left( {{x^2} - 2x + 1} \right) - \left( {{y^2} - 2yz + {z^2}} \right)\\
= {\left( {x - 1} \right)^2} - {\left( {y - z} \right)^2}\\
= \left( {x - 1 - y + z} \right)\left( {x - 1 + y - z} \right)
\end{array}\]

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Answer 2

\[\begin{array}{l}
a){(2 - 3x)^2} - {(3 - x)^2}\\
= \left[ {\left( {2 - 3x} \right) - \left( {3 - x} \right)} \right].\left[ {\left( {2 - 3x} \right) + \left( {3 - x} \right)} \right]\\
= \left( {2 - 3x - 3 + x} \right)\left( {2 - 3x + 3 - x} \right)\\
= \left( { - 1 - 2x} \right)\left( {5 - 4x} \right)\\
b)49{(x - 3)^2} - 9{(x + 2)^2}\\
= {\left( {7x - 21} \right)^2} - {\left( {3x + 6} \right)^2}\\
= \left[ {\left( {7x - 21} \right) - \left( {3x + 6} \right)} \right].\left[ {\left( {7x - 21} \right) + \left( {3x + 6} \right)} \right]\\
= \left( {7x - 21 - 3x - 6} \right)\left( {7x - 21 + 3x + 6} \right)\\
= \left( {4x - 27} \right)\left( {10x - 15} \right)\\
c)2xy - {x^2} - {y^2} + 16\\
= 16 - \left( {{x^2} - 2xy + {y^2}} \right)\\
= {4^2} - {\left( {x - y} \right)^2}\\
= \left( {4 - x + y} \right)\left( {4 + x - y} \right)\\
d)2(x - 3) + 3({x^2} - 9)\\
= 2\left( {x - 3} \right) + 3\left( {x - 3} \right)\left( {x + 3} \right)\\
= \left( {x - 3} \right)\left( {2 + 3x + 9} \right)\\
= \left( {x - 3} \right)\left( {3x + 11} \right)\\
e)16{x^2} - {({x^2} + 4)^2}\\
= {\left( {4x} \right)^2} - {\left( {{x^2} + 4} \right)^2}\\
= \left( {4x - {x^2} - 4} \right)\left( {4x + {x^2} + 4} \right)\\
= - {\left( {x - 2} \right)^2}{\left( {x + 2} \right)^2}\\
f)1 - 2x + 2yz + {x^2} - {y^2} - {z^2}\\
= \left( {{x^2} - 2x + 1} \right) - \left( {{y^2} - 2yz + {z^2}} \right)\\
= {\left( {x - 1} \right)^2} - {\left( {y - z} \right)^2}\\
= \left( {x - 1 - y + z} \right)\left( {x - 1 + y - z} \right)
\end{array}\]

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