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Giải bài 1.37 trang 25 SGK Toán 8 - Cùng khám phá

a) Chứng minh rằng:
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Đề bài

a) Chứng minh rằng: \({a^3} + {b^3} = {\left( {a + b} \right)^3} - 3ab\left( {a + b} \right).\) b) Tính giá trị của \({a^3} + {b^3},\) biết rằng \(a + b = 5\) và \(ab =  - 6.\)

Phương pháp giải - Xem chi tiết

Sử dụng hằng đẳng thức kết hợp với nhân đa thức với đa thức.

Lời giải chi tiết

a) Ta có: \(VP = {a^3} + 3{a^2}b + 3a{b^2} + {b^3} - 3{a^2}b - 3a{b^2} = {a^3} + {b^3} = VT\left( {dpcm} \right)\)b) Thay \(a + b = 5\) và \(ab =  - 6.\) vào biểu thức, ta có\({a^3} + {b^3} = {\left( {a + b} \right)^3} - 3ab\left( {a + b} \right) = {5^3} - 3.\left( { - 6} \right).5 = 215.\)Vậy giá trị của biểu thức là \(215.\)

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