Ta có
\(\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)\)
Ta có \(\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)\)
\(=\left(x^2-y^2\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)\)
\(=\left(x^4-y^4\right)\left(x^4+y^4\right)\left(x^8+y^8\right)\)
\(=\left(x^8-y^8\right)\left(x^8+y^8\right)\)
\(=x^{16}-y^{16}\)
Đặt \(A=\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)\)
Áp dụng công thức \(\left(a-b\right)\left(a+b\right)=a^2-b^2\) ta được:
\(\Leftrightarrow A=\left(x^2-y^2\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)\)
\(\Leftrightarrow A=\left(x^4-y^4\right)\left(x^4+y^4\right)\left(x^8+y^8\right)\)
\(\Leftrightarrow A=\left(x^8-y^8\right)\left(x^8+y^8\right)\)
\(\Leftrightarrow A=\left(x^{16}-y^{16}\right)\)
Ta có \(\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)\)
=\(\left(x^2-y^2\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)\)
=\(\left(x^4-y^4\right)\left(x^4+y^4\right)\left(x^8+y^8\right)=\left(x^8-y^8\right)\left(x^8+y^8\right)\)
=\(x^{16}-y^{16}\)