Question

rút gọn biểu thức A=(x+y)(x^2+y^2)(x^4+y^4)...(x^64+y^64) với x-y=1.

các bn lm giúp mk nhá.

Answer 1

\(A=1.\left(x+y\right)\left(x^2+y^2\right)...\left(x^{64}+y^{64}\right)\)

\(=\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)...\left(x^{64}+y^{64}\right)\)

\(=\left(x^2-y^2\right)\left(x^2+y^2\right)\left(x^4+y^4\right)...\left(x^{64}+y^{64}\right)\)

\(=\left(x^4-y^4\right)...\left(x^{64}+y^{64}\right)\)

\(=...=\left(x^{64}-y^{64}\right)\left(x^{64}+y^{64}\right)=x^{128}-y^{128}\)