Question

Разложить на множители многочлен:
381.
1) х^4+2х^2у+у^2
2) р^4-2р^2q+q^2
3)4c^4+12c^2d^3+9d^6
4) 25a^6+30a^3b+9b^2

Answer 1

Объяснение:

${x}^{4} + 2x^{2}y + {y}^{2} = ({x}^{2} + y) ^{2}$

${p}^{4} - {2p}^{2} q + {q}^{2} = ( {p}^{2} - q) ^{2}$

${4c}^{4} + {12c}^{2} {d}^{3} + {9d}^{6} = ( {2c}^{2} + {3d}^{3} ) ^{2}$

${25a}^{6} + {30a}^{3} b + {9b}^{2} = ( {5a}^{3} + 3b) ^{2}$

Answer 2

Ответ:

$x^4+2x^2y+y^2=(x^2)^2+2x^2y+y^2=(x^2+y)^2\\\\p^4-2p^2q+q^2=(p^2)^2-2p^2q+q^2=(p^2-q)^2\\\\4c^4+12c^2d^3+9d^6=(2x^2)^2+2\cdot 2x^2\cdot 3d^3+(3d^3)^2=(2x^2+3d^3)^2\\\\25a^6+30a^3b+9b^2=(5a^3)^2+2\cdot 5a^3+(3b)^2=(5a^3+3b)^2$