Viết mỗi biểu thức sau dưới dạng tích:a) \(25{{\rm{x}}^2} - 16\) b) \(16{{\rm{a}}^2} - 9{b^2}\) c) \(8{{\rm{x}}^3} + 1\)d) \(125{{\rm{x}}^3} + 27{y^3}\) e) \(8{{\rm{x}}^3} - 125\) g) \(27{{\rm{x}}^3} -...
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Viết mỗi biểu thức sau dưới dạng tích:
a) \(25{{\rm{x}}^2} - 16\) b) \(16{{\rm{a}}^2} - 9{b^2}\) c) \(8{{\rm{x}}^3} + 1\)
d) \(125{{\rm{x}}^3} + 27{y^3}\) e) \(8{{\rm{x}}^3} - 125\) g) \(27{{\rm{x}}^3} - {y^3}\)
a) \(25{{\rm{x}}^2} - 16 = {\left( {5{\rm{x}}} \right)^2} - {4^2} = \left( {5{\rm{x}} + 4} \right)\left( {5{\rm{x}} - 4} \right)\)
b) \(8{{\rm{x}}^3} + 1 = {\left( {2{\rm{x}}} \right)^3} + {1^3} = \left( {2{\rm{x}} + 1} \right)\left( {4{{\rm{x}}^2} - 2{\rm{x}} + 1} \right)\)
c) \(8{{\rm{x}}^3} - 125 = {\left( {2{\rm{x}}} \right)^3} - {5^3} = \left( {2{\rm{x}} - 5} \right)\left( {4{{\rm{x}}^2} + 10{\rm{x + }}25} \right)\)
d) \(27{{\rm{x}}^3} - {y^3} = {\left( {3x} \right)^3} - {y^3} = \left( {3{\rm{x}} - y} \right)\left( {9{{\rm{x}}^2} + 3{\rm{x}}y + {y^2}} \right)\)
e) \(16{{\rm{a}}^2} - 9{b^2} = {\left( {4{\rm{a}}} \right)^2} - {\left( {3b} \right)^2} = \left( {4{\rm{a}} - 3b} \right)\left( {4{\rm{a}} + 3b} \right)\)
g) \(125{{\rm{x}}^3} + 27{y^3} = {\left( {5{\rm{x}}} \right)^3} + {\left( {3y} \right)^3} = \left( {5{\rm{x}} + 3y} \right)\left( {25{{\rm{x}}^2} - 15{\rm{x}}y + 9{y^2}} \right)\)