Question

разложите на множители
1) 3m^2n^2-48m^2p^2 2) 3x^2+12xy+12y^2

Answer 1

$1) \: \: 3 {m}^{2} {n}^{2} - 48 {m}^{2} {p}^{2} = 3( {m}^{2} {n}^{2} - 16 {m}^{2} {n}^{2} ) = 3(m - 4n)(m + 4n)$
$2) \: 3 {x}^{2} + 12xy + 12 {y}^{2} = 3 {x}^{2} + 6xy + 6xy + 12 {y}^{2} = (3 {x}^{2} + 6xy) + (12 {y}^{2} + 6xy) = 3x(x + 2y) + 6y(x + 2y) = (x + 2y)(3x + 6y) = 3(x + 2y)(x + 2y) = 3 {(x + 2y}^{2} )$