Question

Решить: 1.9m^2-16n^2 2.4b^4-25a^2 3.(2b+3a)^3 ^ этот символ в квадрате или в кубе

Answer 1

1) 9m²-16n²=(3m-4n)(3m+4n)
2)4b⁴-25a²=(2b²-5a)(2b²+5a)
3)(2b+3a)³=8b³+18b²a+54ba²+27a³

Answer 2

$1)9 {m}^{2} - 16 {n}^{2} = {3}^{2} {m}^{2} - {4}^{2} {n}^{2} = (3m {)}^{2} - (4n {)}^{2} = \\ (3m - 4n) \times (3m + 4n)$
$2)4 {b}^{4} - 25 {a}^{2} = {2}^{2} {b}^{2 \times 2} - {5}^{2} {a}^{2} = \\ {2}^{2} ( {b}^{2} {)}^{2} - (5a {)}^{2} = (2 {b}^{2} {)}^{2} - (5a {)}^{2} = \\ (2 {b}^{2} - 5a) \times (2 {b}^{2} + 5a)$
$3)(2b + 3a {)}^{2} = (2b {)}^{2} + 2 \times 2b \times 3a + (3a {)}^{2} = \\ 4 {b}^{2} + 12ab + 9 {a}^{2}$