Question

Розкладіть на множники.
1) 4аb^3 – а^3b;
2) -9b – 6b^2 – b^3;
3) 27а^2 – a^5;
4)а^2 + 2аb + b^2 – 9

Answer 1

$4ab {}^{3} - a {}^{3} b = ab(4 {b}^{2} - {a}^{2} ) = ab(2b - a)(2b + a)$

$- 9b - 6b {}^{2} - b {}^{3} = - b(9 + 3b + {b}^{2} ) = - b(b + 3) {}^{2}$

$27a {}^{2} - a {}^{5} = a {}^{2} (27 - a {}^{3} ) = {a}^{2} (3 - x)(9 + 3x + x {}^{2} )$

${a}^{2} + 2ab + {b}^{2} - 9 = (a + b) {}^{2} - 9 = (a + b - 3)(a + b + 3)$