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Giải bài 1.19 trang 13 SGK Toán 8 - Cùng khám phá

Chứng minh rằng giá trị của biểu thức sau không phụ thuộc
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Đề bài

Chứng minh rằng giá trị của biểu thức sau không phụ thuộc vào giá trị của biến: \(\left( {1 + x} \right)\left( {1 + y} \right) - x\left( {y + 1} \right) - y + 9\)

Phương pháp giải - Xem chi tiết

Thực hiện nhân đa thức với đa thức, nhân đơn thức với đa thức Rút gọn biểu thức( Rút gọn các đơn thức đồng dạng).

Lời giải chi tiết

\(\begin{array}{l}\left( {1 + x} \right)\left( {1 + y} \right) - x\left( {y + 1} \right) - y + 9 = 1 + x + y + xy - xy - x - y + 9\\ = \left( {x - x} \right) + \left( {xy - xy} \right) + \left( {y - y} \right) + \left( {1 + 9} \right)\\ = 10\end{array}\)Vậy biểu thức trên bằng \(10\) với mọi giá trị của \(x;y\) hay giá trị của biểu thức không phụ thuộc vào giá trị của biến.

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