展开 2(x^2+y^2)^2

解答

展开

2 (x^{2} + y^{2})^{2}

2 x^{4} + 4 x^{2} y^{2} + 2 y^{4}

求解步骤

2 (x^{2} + y^{2})^{2}

展开

(x^{2} + y^{2})^{2} : x^{4} + 2 x^{2} y^{2} + y^{4}

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

使用分配律:

m (a + b + c) = ma + mb + m c

2 (x^{4} + 2 x^{2} y^{2} + y^{4}) = 2 x^{4} + 2 \cdot 2 x^{2} y^{2} + 2 y^{4}

= 2 x^{4} + 2 \cdot 2 x^{2} y^{2} + 2 y^{4}

数字相乘:

2 \cdot 2 = 4

= 2 x^{4} + 4 x^{2} y^{2} + 2 y^{4}

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