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\(4a^2-4ab-8b^2\)
\(=4\left(a^2-ab-2b^2\right)\)
\(=4\left(a^2-ab-b^2-b^2\right)\)
\(=4\left[\left(a^2-b^2\right)-\left(ab+b^2\right)\right]\)
\(=4\left[\left(a-b\right)\left(a+b\right)-b\left(a+b\right)\right]\)
\(=4\left(a+b\right)\left(a-b-b\right)\)
\(=4\left(a+b\right)\left(a-2b\right)\)
\(a^2-2.a.2b+4b^2-5b^2=\left(a-2b\right)^2-5b^2..\)
\(=\left(a-2b-b\sqrt{5}\right)\left(a-2b+b\sqrt{5}\right)\)
\(a^6-a^4+2a^3+2a^2\)
\(=\left[\left(a^3\right)^2-\left(a^2\right)^2\right]+2\left(a^2+a^3\right)\)
\(=\left(a^3-a^2\right)\left(a^3+a^2\right)+2\left(a^3+a^2\right)\)
\(=\left(a^3-a^2+2\right)\left(a^3+a^2\right)\)
\(=a^2.\left(a^3-a^2+2\right)\left(a+1\right)\)
\(a^6-a^4+2a^3+2a^2=a^2\left(a^4-a^2+2a+2\right)=a^2\left[a^2\left(a^2-1\right)+2\left(a+1\right)\right]\)
\(=a^2\left[a^2\left(a-1\right)\left(a+1\right)+2\left(a+1\right)\right]=a^2\left(a+1\right)\left(a^3-a^2+2\right)=a^2\left(a+1\right)^2\left(a^2-2a+2\right)\)
\(36\left(a-b\right)^2-25\left(2a-1\right)^2=\left[6\left(a-b\right)\right]^2-\left[5\left(2a-1\right)\right]^2\)
\(=\left(6a-6b\right)^2-\left(10a-5\right)^2=\left(6a-6b-10a+5\right)\left(6a-6b+10a-5\right)\)
\(=\left(-4a-6b+5\right)\left(16a-6b-5\right)\)