展开 (0.5x^2y^3+0.7a^2b^2)^2

解答

展开

(0.5 x^{2} y^{3} + 0.7 a^{2} b^{2})^{2}

0.25 x^{4} y^{6} + 0.7 x^{2} y^{3} a^{2} b^{2} + 0.49 a^{4} b^{4}

求解步骤

(0.5 x^{2} y^{3} + 0.7 a^{2} b^{2})^{2}

使用完全平方公式:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(0.5 x^{2} y^{3} + 0.7 a^{2} b^{2})^{2} = (0.5 x^{2} y^{3})^{2} + 2 \cdot 0.5 x^{2} y^{3} \cdot 0.7 a^{2} b^{2} + (0.7 a^{2} b^{2})^{2}

= (0.5 x^{2} y^{3})^{2} + 2 \cdot 0.5 x^{2} y^{3} \cdot 0.7 a^{2} b^{2} + (0.7 a^{2} b^{2})^{2}

化简

(0.5 x^{2} y^{3})^{2} + 2 \cdot 0.5 x^{2} y^{3} \cdot 0.7 a^{2} b^{2} + (0.7 a^{2} b^{2})^{2} : 0.25 x^{4} y^{6} + 0.7 x^{2} y^{3} a^{2} b^{2} + 0.49 a^{4} b^{4}

= 0.25 x^{4} y^{6} + 0.7 x^{2} y^{3} a^{2} b^{2} + 0.49 a^{4} b^{4}

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