Question

разложите на множители:
a)4x^2y^2-9a^4
d)25a^2-(a+3)^2
Помогите пожалуйста

Answer 1

a)

$\displaystyle \tt 4 {x}^{2} {y}^{2} - 9 {a}^{4} = {2}^{2} {x}^{2} {y}^{2} - {3}^{2} {a}^{2 \cdot2} = {(2xy)}^{2} - {3}^{2} \cdot {( {a}^{2}) }^{2} = {(2xy)}^{2} - {(3 {a}^{2} )}^{2} = \bold{(2xy - 3 {a}^{2} )(2xy + 3 {a}^{2}) }$

d)

$\displaystyle \tt 25 {a}^{2} - {(a + 3)}^{2} = (5a - (a + 3))(5a + (a + 3)) = (5a - a - 3)(5a + a + 3) = \\ \\ \displaystyle \tt = (4a - 3)(6a + 3) = (4a - 3) \cdot3(2a + 1) = \bold{3(4a - 3)(2a + 1)}$