▪1) 28a^2 - 175b^2 = 7(4a^2 - 25b^2) = 7(2a - 5b)(2a + 5b)
▪2) 3xy^3 - 48(x^3)y = 3xy(y^2 - 16x^2) = 3xy(y - 4x)(y + 4x)
▪3) x^4 - 81 =(x^2)^2 - 9^2 = (x^2 - 9)(x^2 + 9)= (x - 3)(x + 3)(x^2 + 9)= (x - 3)(x + 3)(x - √6х + 3)(x + √6х + 3)
▪4) (b^3)c - 5b^2 -bc^3 + 5c^2 = b^2(bc - 5) - c^2(bc - 5) = (b^2 - c^2)(bc - 5) = (b - c)(b + c)(bc - 5)
▪5) 4b^2 - 2b - a^2 + a = (2b - a)(2b + a) - (2b - a) = (2b - a)(2b + a - 1)
▪6) 2ac^2 + c^3 - 18a^3 - 9(a^2)c = 2a(c^2 - 9a^2) + c(c^2 - 9a^2) = (c^2 - 9a^2)(2a + c) = (c - 3a)(c + 3a)(2a + c)
▪7) 112a^3 - 175a = 7a(16a^2 - 25) = 7a(4a - 5)(4a + 5)
▪8) m^13 + mn^9 = m(m^12 + n^9) = m((m^4)^3 + (n^3)^3) = m(m^4 + n^3)(m^8 - (m^4)(n^3) + n^6)
▪9) 8 + 14b - 7b^2 - b^3 = 8 + 7b(2 - b) - b^3 = 2^3 - b^3 + 7b(2 - b) = (2 - b)(4 + 2b +b^2) + 7b(2 - b) = (2 - b)(4 + 2b +b^2 + 7b) = (2 - b)(4 + 9b +b^2)
▪10) 64a^6 - b^6 = (2a)^6 - b^6 = (8a^3)^2 - (b^3)^2 = (8a^3 - b^3)(8a^3 + b^3) = (2a - b)(4a^2 + 2ab + b^2)(2a + b)(4a^2 - 2ab + b^2);
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