化简 (a^2+b^2)^2*(a^2-b^2)^2

解答

化简

(a^{2} + b^{2})^{2} \cdot (a^{2} - b^{2})^{2}

(a^{2} + b^{2})^{2} (a^{2} - b^{2})^{2}

求解步骤

(a^{2} + b^{2})^{2} (a^{2} - b^{2})^{2}

使用指数法则:

a^{m} b^{m} = (ab)^{m},

假定

a \geq 0, b \geq 0

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

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

使用指数法则:

(a \cdot b)^{n} = a^{n} b^{n}

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

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