How do you factor $1029 y x^{3} + 24 y^{4}$ $1029yx^3 + 24y^4$ ?

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Answer 1 · 2015-05-12T14:09:12

$1029 y x^{3} + 24 y^{4} = 3 y (343 x^{3} + 8 y^{3})$ $1029yx^3+24y^4=3y(343x^3+8y^3)$

$= 3 y ({(7 x)}^{3} + {(2 y)}^{3})$ $=3y((7x)^3+(2y)^3)$

$= 3 y (7 x + 2 y) ({(7 x)}^{2} - (7 x) (2 y) + {(2 y)}^{2})$ $=3y(7x+2y)((7x)^2-(7x)(2y)+(2y)^2)$

$= 3 y (7 x + 2 y) (49 x^{2} - 14 x y + 4 y^{2})$ $=3y(7x+2y)(49x^2-14xy+4y^2)$

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

There are linear factors of $(49 x^{2} - 14 x y + 2 y^{2})$ $(49x^2-14xy+2y^2)$ , but they have Complex coefficients.

How do you factor 1029yx^3 + 24y^41029yx3+24y41029yx^3 + 24y^4?