1) 3mn^2-12m-5n^2+20
2)9-4x^2-48xy-144y^2
3)xy^3-y^3-8x+8
4)243x^5-32
Задание разложите на множители
2)9-4x^2-48xy-144y^2
3)xy^3-y^3-8x+8
4)243x^5-32
Задание разложите на множители
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Answers & Comments
Verified answer
3mn² - 12m - 5n² + 20 = 3m* n² - 3m * 4 - 5 *n² - 5 * (-4) == 3m(n² - 4) - 5(n² - 4) = (3m - 5)(n² - 4) = (3m - 5)(n² - 2²) =
= (3m - 5)(n - 2)(n + 2)
9 - 4x² - 48xy - 144y² = 3² - ((2x)² - 2*2x *12y + (12y)²) =
= 3² - (2x - 12y)² = - ( (2x - 12y)² - 3² ) =
= - (2x - 12y - 3)(2x -12y + 3)
xy³ - y³ - 8x + 8 = y³(x - 1) - 8(x - 1) = (x-1)(y³ - 8) =
= (x - 1)(y³ - 2³) = (x - 1)(y - 2)(y² + y*2 + 2² ) =
= (x - 1)(y - 2)(y² +2y + 4)
243x⁵ - 32 = (3x)⁵ - 2⁵ = (3x - 2)( (3x)⁴ + (3x)³ *2 +(3x)² * 2² + 3x *2³ + 2⁴) =
=(3x - 2)(81x⁴ + 54x³ + 36x² + 24x + 16)