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Giải bài 7 trang 32 vở thực hành Toán 8

Chứng minh rằng giá trị của biểu thức sau không phụ thuộc vào giá trị của biến x.

Tổng hợp đề thi học kì 2 lớ💜p 8 tất cả các môn - Kết nối tr💫i thức

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

Chứng minh rằng giá trị của ✤biểu thức sau không phụ꧅ thuộc vào giá trị của biến x.

\(A = {\left( {x + 3} \right)^3}♚ - {\left( {x - 3} \right💎)^3} - 18{x^2}\).

Phương pháp giải - Xem chi tiết

Rút gọn A bằng cách sử dụng hằng đẳng thức:

- Sử dụng hằn🎀g đẳng thức lập phương củ꧟a một tổng: \({(a + b)^3} = {a^3} + 3{a^2}b + 3a{b^2} + {b^3}\)

- Sử dụng hằng đẳng th🐓ức lập phương của một hiệu: \({(a - b)^3} = {a^3} - 3{a^2}b + 3a{b^2} - {b^3}\)

Lời giải chi tiết

Ta có 

\(\begin{array}{l}A = \left( {{x^3} + 3.{x^2}.3 + 3.x{{.3}^2} + {3^3}} \right) - \left( {{x^3} - 3.{x^2}.3 + 3.x{{.3}^2} - {3^3}} \right) - 18{x^2}\🍒\ = {x^3} + 9{x^2} + 27x + 27 - {x^3} + 9{x^2} - 27x + 27 - 18{x^2}\\ = \left( {{x^3} - {x^3}} \right) + \left( {9{x^2} + 9{x^2} - 18{x^2}} \right) ♒+ \left( {27x - 27x} \right) + \left( {27 + 27} \right)\\ = 54\end{array}\)

Vậy giá trị của biểu thức A không phụ thuộc vào biến x🌜.

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