a) Ta có: \(a^6-a^4+2a^3+2a^2\)
\(=a^4\left(a^2-1\right)+2a^2\left(a+1\right)\)
\(=a^4\left(a+1\right)\left(a-1\right)+2a^2\left(a+1\right)\)
\(=\left(a+1\right)\left(a^5-a^4+2a^2\right)\)
\(=a^2\left(a+1\right)\left(a^3-a^2+2\right)\)
b) Ta có: \(x^6-x^4+2x^3+2x^2\)
\(=x^4\left(x^2-1\right)+2x^2\left(x+1\right)\)
\(=x^4\left(x-1\right)\left(x+1\right)+2x^2\left(x+1\right)\)
\(=x^2\left(x+1\right)\left(x^3-x^2+2\right)\)
c) Ta có: \(\left(2x+2\right)^2+2\left(2x+2\right)\left(2x-2\right)+\left(2x-2\right)^2\)
\(=\left(2x+2+2x-2\right)^2\)
\(=\left(4x\right)^2=16x^2\)
a) \(a^6-a^4+2a^3+2a^2\)
\(=\left(a^3\right)^2-\left(a^2\right)^2+2a^3+2a^2-1+1\)
\(=\left[\left(a^3\right)^2+2a^3+1\right]-\left[\left(a^2\right)^2-2a^2+1\right]\)
\(=\left(a^3+1\right)^2-\left(a^2-1\right)^2\)
\(=\left(a^3+1-a^2+1\right)\left(a^3+1+a^2-1\right)\)
\(=\left(a^3-a^2+2\right)\left(a^3+a^2\right)\)
b/ \(x^6-x^4+2x^3+2x^2\)
\(=\left(x^3\right)^2-\left(x^2\right)^2+2x^3+2x^2-1+1\)
\(=\left[\left(x^3\right)^2+2x^3+1\right]-\left[\left(x^2\right)^2-2x^2+1\right]\)
\(=\left(x^3+1\right)^2-\left(x^2-1\right)^2\)
\(=\left(x^3+1-x^2+1\right)\left(x^3+1+x^2-1\right)\)
\(=\left(x^3-x^2+2\right)\left(x^3+x^2\right)\)
c/ \(\left(2x+2\right)^2+2\left(2x+2\right)\left(2x-2\right)+\left(2x-2\right)^2\)
\(=4x^2+8x+4+2\left(4x^2-4\right)+4x^2-8x+4\)
\(=4x^2+8x+4+8x^2-8+4x^2-8x+4\)
\(=16x^2\)