Question

Разложить на множители
1) 8xy^2-4y^2+2x^2y-xy =?
2) 3x^3-5x^2y-9x+15y=?
3) m^3n^2-m+m^2n^3-n=?
4) ax^2+ay-cy+bx^2-cx^2+by=?

Answer 1

Объяснение:

1)

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

2)

$3 {x}^{3} - 5 {x}^{2} y - 9x + 15y \\ 3 {x}^{3} - 9x + 15y - 5{x}^{2} y \\ 3x( {x}^{2} - 3) - 5y( {x}^{2} - 3) \\ ( {x}^{2} - 3)(3x - 5y)$

3)

${m}^{3} n {}^{2} - m + {m}^{2} {n}^{3} - n \\ {m}^{3} n {}^{2} + {m}^{2} {n}^{3} - m - n \\ m {}^{2} {n}^{2} (m + n) - 1(m + n) \\ (m + n)(m {}^{2} {n}^{2} - 1)$

4)

$a {x}^{2} + ay - cy + b {x}^{2} - c {x}^{2} + by \\ a {x}^{2} + ay + bx {}^{2} + by - c {x}^{2} - cy \\ a( {x}^{2} + y) + b( {x}^{2} + y) - c( {x}^{2} + y) \\ ( {x}^{2} + y)(a + b - c)$

Наверно так, если в условии написано так