Đề kiểm tra 15 phút - Đề số 5 - Bài 9 - Chương 1 - Đại số 8

a) \({\left( {a + b} \right)^2} - {m^2} + a + b - m\)

b) \({x^3} - 6{x^2} + 12x - 8\)

c) \({x^2} - 7xy + 10{y^2}\)

d) \({x^4} + 2{x^3} - 4x - 4 = 0.\)

a) \({\left( {a + b} \right)^2} - {m^2} + a + b - m \)

\(= \left( {a + b + m} \right)\left( {a + b - m} \right) + \left( {a + b - m} \right)\)

\( = \left( {a + b - m} \right)\left( {a + b + m + 1} \right).\)

b) \({x^3} - 6{x^2} + 12x - 8 = {\left( {x - 2} \right)^3}\)

Cách khác:

\({x^3} - 6{x^2} + 12x - 8\)

\(= \left( {{x^3} - 8} \right) - 6x\left( {x - 2} \right)\)

\( = \left( {x - 2} \right)\left( {{x^2} + 2x + 4 - 6x} \right)\)

\(= {\left( {x - 2} \right)^3}\)

c) \({x^2} - 7xy + 10{y^2} \)

\(= {x^2} - 2xy - 5xy + 10{y^2}\)

\(= x\left( {x - 2y} \right) - 5y\left( {x - 2y} \right)\)

\( = \left( {x - 2y} \right)\left( {x - 5y} \right).\)

d) \({x^4} + 2{x^3} - 4x - 4 \)

\(= \left( {{x^4} - 4} \right) + \left( {2{x^3} - 4x} \right) \)

\(= \left( {{x^2} - 2} \right)\left( {{x^2} + 2} \right) + 2x\left( {{x^2} - 2} \right)\)

\( = \left( {{x^2} - 2} \right)\left( {{x^2} + 2 + 2x} \right) \)

\(= \left( {x - \sqrt 2 } \right)\left( {x + \sqrt 2 } \right)\left( {{x^2} + 2x + 2} \right).\)