Question

2. FACTORIZAR
 x2 +16x +15 =
 m2 – 9m +18 =
 x3 + 12x + 8 + 6x2=
 4p2 + 12p + 9=
 4m4 – 29m2n2 +25n4 =

Answer 1

Explicación paso a paso:

${x}^{2} + 16x + 15 = (x + 15)(x + 1) \\ {m}^{2} - 9m + 18 = (m - 6)(m - 3) \\ {x}^{3} + 6 {x}^{2} + 12x + 8 = ( {x + 2)}^{3} \\ 4 {p}^{2} + 12p + 9 = ( {2p + 3)}^{2}$

$4 {m}^{4} - 29 {m}^{2} {n}^{2} + 25 {n}^{4} \\ = 4 {m}^{4} - 29 {m}^{2} {n}^{2} + 9 {m}^{2} {n}^{2} + 25 {n}^{4} - 9 {m}^{2} {n}^{2} \\ = 4 {m}^{4} - 20 {m}^{2} {n}^{2} + 25 {n}^{4} - 9 m^{2} {n}^{2} \\ = (4 {m}^{4} - 20 {m}^{2} {n}^{2} + 25 {n}^{4} ) - 9 {m}^{2} {n}^{2} \\ = ( {2 {m}^{2} - 5 {n}^{2} ) }^{2} - 9 {m}^{2} {n}^{2} \\ =( (2 {m}^{2} - 5 {n}^{2} ) + 3mn)((2 {m}^{2} - 5 {n}^{2} ) - 3mn) \\ = (2 {m}^{2} + 3mn - 5 {n}^{2} )(2 {m}^{2} - 5 {n}^{2} - 3mn)$