Question

Упростите:(2x^2+y)(4x^4-2x^2y+y^2)(64x^12-8x^6y^3+y^6)

Answer 1

$(2x^{2}+y)(4x^{4}-2x^{2}y+y^{2})(64x^{12}-8x^{6}y^{3}+y^{6})=$

$=(2x^{2}+y)(((2x^{2})^{2}-(2x^{2})y+y^{2})((8x^{6})^{2}-8x^{6}y^{3}+(y^{3})^{2})=$

$=((2x^{2})^{3}+y^{3})((8x^{6})^{2}-8x^{6}y^{3}+(y^{3})^{2})=$

$=(8x^{6}+y^{3})((8x^{6})^{2}-8x^{6}y^{3}+(y^{3})^{2})=(8x^{6})^{3}+(y^{3})^{3}=$

$=512x^{18}+y^{9}$