Question

Rút gọn biểu thức:

a) P= (5x-1)+2x(1-5x)x(4+5x)+(5x+4)^2

b) Q= (x-y)^3+(y+x)^3+(y-x)^3-3xy(x+y)

c) 12(5^2+1)(5^4+1)(5^8+1)(5^16+1)

Answer 1

a: \(P=\left(5x-1-5x-4\right)^2=\left(-3\right)^2=9\)

b: \(Q=\left(x+y\right)^3-3xy\left(x+y\right)=x^3+y^3\)

c: \(=\dfrac{\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)

\(=\dfrac{\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)

\(=\dfrac{\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)

\(=\dfrac{5^{32}-1}{2}\)