Question

помогите пожалуйста ​

Answer 1

${x}^{3} + 125 {y}^{3} = {x}^{3} + (5y) {}^{3} = (x + 5y)(x {}^{2} - 5xy + 25 {y}^{2} )$

$- 5 {x}^{2} + 30x - 45 = - 5( {x}^{2} - 6x + 9) = - 5(x - 3) {}^{2}$

${a}^{5} - a = a(a {}^{4} - 1) = a(a {}^{2} - 1)(a {}^{2} + 1) = a(a - 1)(a + 1)(a {}^{2} + 1)$

$a + b + {a}^{2} - {b}^{2} = (a + b) + (a + b)(a - b) = (a + b)(a - b + 1)$

${x}^{2} + 8xy + 16y {}^{2} - 1 = (x + 4y) {}^{2} - 1 = (x + 4y - 1)(x + 4y + 1)$

$5 {x}^{3} - 5 {y}^{3} = 5( {x}^{3} - {y}^{3} ) = 5(x - y)(x {}^{2} + xy + {y}^{2} )$