Question

Разложите выражения на множители:
(4x^2 + 9y^2)^2 − 144x^2y^2
x^3 + 9x^2 +27x - 19

Answer 1

Ответ:

1. $16x^{4}{-72x^{2}y^{2}}}+81y^{4}$

2. ${(x-1)(x^{2}-8x+19)}}$

Объяснение:

1.

$(4x^{2}+9y^{2})^{2}-144x^{2}y^{2}=(4x^{2}+9y^{2})(4x^{2}+9y^{2})}}-144x^{2}y^{2}=\\={4(4x^{2}+9y^{2})x^{2}+9(4x^{2}+9y^{2})y^{2}}}-144x^{2}y^{2}=\\={16x^{4}+36x^{2}y^{2}}}+9(4x^{2}+9y^{2})y^{2}-144x^{2}y^{2} =16x^{4}+36x^{2}y^{2}+{36x^{2}y^{2}+81y^{4}}}-144x^{2}y^{2}=\\=16x^{4}+{72x^{2}y^{2}}}+81y^{4}-144x^{2}y^{2}=\\=16x^{4}{-72x^{2}y^{2}}}+81y^{4}$

2.

$x^{3}-9x^{2}+27x-19=\\=x^{3}-8x^{2}+19x-1x^{2}+8x-19=\\={x(x^{2}-8x+19)}}{-1(x^{2}-8x+19)}}=\\={(x-1)(x^{2}-8x+19)}}$