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a, \(3a^2b^2-6a^2b^3+3a^2b^2\)
\(=6a^2b^2-6a^2b^3=6a^2b^2\left(1-b\right)\)
b, \(a^{n+1}-2a^{n-1}=a^2.a^{n-1}-2a^{n-1}=a^{n-1}\left(a^2-2\right)\)
c, \(3a^2b\left(a+b-2\right)-4ac^2-4bc^2+8c^2\)
\(=3a^2b\left(a+b-2\right)-4c^2\left(a+b-2\right)\)
\(=\left(3a^2b-4c^2\right)\left(a+b-2\right)\)
c, \(5a^n\left(a^2-ab+1\right)-2a^2b^n+2ab^{n+1}-2b^n\)
\(=5a^n\left(a^2-ab+1\right)-2a^2b^n+2ab^n.b-2b^n\)
\(=5a^n\left(a^2-ab+1\right)-2b^n\left(a^2-ab+1\right)\)
\(=\left(5a^n-2b^n\right)\left(a^2-ab+1\right)\)
\(3y^2\left(a-3x\right)-a\left(a-3x\right)=\left(3y^2-a\right)\left(a-3x\right)\)
b)\(2a^2-3+5a\)
\(=\left(2a^2+6a\right)-\left(a+3\right)\)
\(=\left(a+3\right)\left(2a-1\right)\)
d)\(2a^2-5-3a\)
\(=\left(2a^2+2a\right)-\left(5a+5\right)\)
\(=\left(a+1\right)\left(2a-5\right)\)
a) \(a^2-3-2a\)
\(=a^2-2a+1-4\)
\(=\left(a^2-2a+1\right)-2^2\)
\(=\left(a-1\right)^2-2^2\)
\(=\left(a-1-2\right)\left(a-1+2\right)\)
\(=\left(a-3\right)\left(a+1\right)\)
c) \(4a+a^2+3\)
\(=a^2+4a+4-1\)
\(=\left(a^2+4a+4\right)-1^2\)
\(=\left(a+2\right)^2-1^2\)
\(=\left(a+2-1\right)\left(a+2+1\right)\)
\(=\left(a+1\right)\left(a+3\right)\)
\(7a\left(3a-5\right)+\left(2a-3\right)\left(4a+1\right)-\left(6a-2\right)^2\)
\(=21a^2-35a+8a^2+2a-12a-3-36a^2+24a-4\)
\(=-7a^2+4a-7\)
a. 3a(2a+b)=6a2+3ab
b. (4a5-12a3+6a2):2a2=2a3-6a+3