a) \(3x^2-11x+6=\left(3x^2-9x\right)-\left(2x-6\right)=\left(x-3\right)\left(3x-2\right)\)

b) \(x^2-7x+12=\left(x^2-3x\right)-\left(4x-12\right)=\left(x-3\right)\left(x-4\right)\)

c) \(3x^2+13x-10=\left(3x^2+15x\right)-\left(2x+10\right)=\left(x+5\right)\left(3x-2\right)\)

d) \(x^2-5x-24=\left(x^2-8x\right)+\left(3x-24\right)=\left(x-8\right)\left(x+3\right)\)

e) \(2x^2-5x-12=\left(2x^2-8x\right)+\left(3x-12\right)=\left(x-4\right)\left(2x+3\right)\)

g) \(x^2-10x+16=\left(x^2-2x\right)-\left(8x-16\right)=\left(x-2\right)\left(x-8\right)\)

\(L=\left\{1;3;5;7;9;11;...\right\}\)

Ta có \(x=a^2+2ab+b^2=\left(a+b\right)^2;y=a^2-2ab+b^2=\left(a-b\right)^2\)

\(2y-x-\left\{2x-y-\left[y+3x-\left(5y-x\right)\right]\right\}\\ =2y-x-\left\{2x-y-\left(y+3x-5y+x\right)\right\}\\ =2y-x-\left(2x-y-y-3x+5y-x\right)\\ =2y-x-2x+y+y+3x-5y+x\\ =x-y\\ =\left(a+b\right)^2-\left(a-b\right)^2\\ =\left(a+b+a-b\right)\left(a+b-a+b\right)\\ =4ab\)