Question

Представьте многочлен в виде произведения:1)2x^2+4xy+2y^22)6x^2-12xy+6y^23)3a^2-6a+34)5m^2+10m+55)2xy^2+4xy+2x6)3a-6ab+3ab^2

Answer 1

$1)2 {x}^{2} +4xy+2 {y}^{2} = \\ = 2( {x}^{2} + 2xy + {y}^{2}) = \\ 2(x + y)(x + y)$
$2)6 {x}^{2} -12xy+6 {y}^{2} = \\ = 6( {x}^{2} -2xy + {y}^{2} ) = \\ = 6(x - y)(x - y)$
$3)3 {a}^{2} -6a+3 = \\ = 3( {a}^{2} - 2a + 1) = \\ = 3(a - 1)(a - 1)$
$4)5 {m}^{2} +10m+5 = \\ = 5( {m}^{2} + 2m + 1) = \\ = 5(m + 1)(m + 1)$
$5)2x {y}^{2} +4xy+2x = \\ = 2x( {y}^{2} + 2y + 1) = \\ = 2x(y + 1)(y + 1)$
$6)3a-6ab+3a {b}^{2} = \\ = 3a(1 - 2b + {b}^{2} ) = \\ = 3a(1 - b)(1 - b)$