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Home » Spider Woman: The Untold Story of the Hero Who Inspired a Generation! - Leaselab

Spider Woman: The Untold Story of the Hero Who Inspired a Generation! - Leaselab

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 Subtract \(-3\) from both sides:

📌 Subtract \( k \) from both sides:

📌 = 8k \quad \Rightarrow \quad k = 0

📌 A science fiction writer models the growth of a resource-dependent colony on Mars using the equation \( a + b = 12 \) and \( a^2 + b^2 = 80 \). Find \( a^3 + b^3 \).

📌 a + b = 12 \quad \text{and} \quad a^2 + b^2 = 80

📌 Use the identity:

📌 We know \( (a + b)^3 = 12^3 = 1728 \). To use the identity, we need \( ab \). From the identity:

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Let $ A = x^2 + 4 $, $ B = y^2 + 2 $, and $ C = y^2 - 2 $, then:
A^2 - 16BC = (A - 4\sqrt{BC})(A + 4\sqrt{BC})
But this factoring is not ideal over real numbers. Instead, observe th...
So the full expression becomes:
Now factor the remaining terms:
Letâs try factoring by grouping. Try factoring $ x^4 + 8x^2 + 16 $ a...
x^4 + 8x^2 + 16 = (x^2 + 4)^2
-16y^4 + 64 = -16(y^4 - 4) = -16(y^2 - 2)(y^2 + 2)
Letâs now expand and factor directly:
x^4 + 8x^2 + 16 - 16y^4 + 64 = x^4 + 8x^2 + 80 - 16y^4

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