Question

Разложите многочлен на множели 48p^3+6=

9x^2+6xy+y^2+12x^2y-4xy^2=

a^2+2ab+b^2-a-b=

Answer 1

$48p^3+6 = 6(8 {p}^{3} + 1) = \\ = 6(2p + 1)(4 {p}^{2} - 2p + 1) \\ \\ 9x^2+6xy+y^2+12x^2 + 4xy^2= \\ = (9x^2+6xy+y^2)+(12x^2y + 4xy^2) = \\ = {(3x + y)}^{2} + 4xy(3x + y) = \\ = (3x + y)(3x + y + 4xy)\\ \\ a^2+2ab+b^2-a-b= \\ = (a^2+2ab+b^2)-(a + b) = \\ = {(a + b)}^{2} - (a + b) = \\ = (a + b)(a + b - 1)$