Основные формулы:
a^2-b^2 = (a+b)(a-b)
(a+b)^2 = a^2 + 2ab + b^2
(a-b)^2 = a^2 - 2ab + b^2
4-5) (a^2 + 1)^2-4a^2 = (a^2+1+2a)(a^2+1-2a) = (a+1)^2*(a-1)^2 = (a^2 - 1)^2
4-6) a^2-2ab+b^2-c^2= (a-b)^2 - c^2 = (a-b+c)(a-b-c)
4-7) 81a^2-16(2a-3b)^2= (9a)^2 - (4(2a-3b))^2 = (9a+4(2a-3b))(9a-4(2a-3b)) = (9a+8a-12b)(9a-8a+12b) = (17a-12b)(a+12b)
4-8) 9-x^2+2xy-y^2= 9 - (x^2-2xy+y^2) = 3^2 - (x-y)^2 = (3+x-y)(3-(x-y)) = (3+x-y)(3-x+y)
4-9) m^3-m^2n-mn^2+n^3 = m^2(m-n) - n^2(m-n) = (m^2-n^2)(m-n) = (m+n)(m-n)(m-n) = (m+n)(m-n)^2
4-10) x^5 - x^3 + x^2 - 1 = x^2(x^3+1) - (x^3+1) = (x^3+1)(x^2-1)