化简 (sqrt(36+a^2)+sqrt(64+b^2))^2

解答

化简

(36 + a^{2} + 64 + b^{2})^{2}

a^{2} + b^{2} + 2 36 + a^{2} 64 + b^{2} + 100

求解步骤

(36 + a^{2} + 64 + b^{2})^{2}

使用完全平方公式:

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

(36 + a^{2} + 64 + b^{2})^{2} = (36 + a^{2})^{2} + 2 36 + a^{2} 64 + b^{2} + (64 + b^{2})^{2}

= (36 + a^{2})^{2} + 2 36 + a^{2} 64 + b^{2} + (64 + b^{2})^{2}

化简

(36 + a^{2})^{2} + 2 36 + a^{2} 64 + b^{2} + (64 + b^{2})^{2} : a^{2} + b^{2} + 2 36 + a^{2} 64 + b^{2} + 100

= a^{2} + b^{2} + 2 36 + a^{2} 64 + b^{2} + 100

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