4-11) (a+b)^4 - (a-b)^4 = ((a+b)^2 + (a-b)^2)((a+b)^2-(a-b)^2) = (a^2+2ab+b^2+a^2-2ab+b^2)(a^2+2ab+b^2-a^2+2ab-b^2) = (2a^2+2b^2)*4ab = 8ab*(a^2+b^2)
4-12) a^6 - a^4 + 2a^3 + 2a^2 = a^4(a^2-1) + 2a^2(a+1) = a^4*(a+1)(a-1) + 2a^2*(a+1) = (a+1)*(a^4(a-1) + 2a^2) = (a+1)*(a^5-a^4+2a^2) = a^2*(a+1)*(a^3-a^2+2)
4-13) a^2 - 7ab + 12b^2 = a^2 - 6ab + 9b^2 - ab + 3b^2 = (a-3b)^2 - b(a-3b) = (a-3b)*(a-3b - b) = (a-3b)*(a-4b)