Question

Разложите на множители.
1)3a^2-2a-12b^2+4b
2)a^3-3a^2+3a-1.

Answer 1

1.

$3 {a}^{2} - 2a - 12 {b}^{2} + 4b = - 3(4 {b}^{2} - {a}^{2} ) + 2(2b -a) = - 3(2b - a) \times (2b + a) + 2(2b -a) = - (2b - a) \times (3(2b + a) - 2) = - (2b - a) \times (6b + 3a - 2)$

2.

${a}^{ 3} - 3 {a}^{2} + 3a - 1 = {a}^{3} - 3 \times {a}^{2} \times 1 + 3 \times a \times 1 - {1}^{3} = {a}^{3} - 3 \times {a}^{2} \times 1 + 3 \times a \times {1}^{2} - {1}^{3} = (a - 1)^{ 3}$