a: \(\left(1-4x\right)\left(1+4x\right)=1-\left(4x\right)^2=1-16x^2\)
b: \(\left(-2x-5y\right)\left(2x-5y\right)\)
\(=-\left(2x+5y\right)\left(2x-5y\right)\)
\(=-\left(4x^2-25y^2\right)=-4x^2+25y^2\)
c: \(\left(x^3-3x\right)\left(x^3+3x\right)=\left(x^3\right)^2-\left(3x\right)^2=x^6-9x^2\)
d: \(\left(1+x+x^2\right)\left(1+x-x^2\right)\)
\(=\left(1+x\right)^2-x^4=-x^4+x^2+2x+1\)
a: \(\left(x^2+4y^2\right)\left(x+2y\right)\left(x-2y\right)\)
\(=\left(x^2+4y^2\right)\left(x^2-4y^2\right)\)
\(=x^4-16y^4\)
b: \(\left(x-1\right)\left(x+1\right)\left(x^2+1\right)\left(x^4+1\right)\)
\(=\left(x^2-1\right)\left(x^2+1\right)\left(x^4+1\right)\)
\(=\left(x^4-1\right)\left(x^4+1\right)\)
\(=x^8-1\)
