Simplify the expression $$(5z - 12y)^2 + (12z + 5y)^2 - 144z^2$$

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**Solution:**

1. Expand each square term using the identity $(a - b)^2 = a^2 - 2ab + b^2$ and $(a + b)^2 = a^2 + 2ab + b^2$:

- $(5z - 12y)^2 = (5z)^2 - 2 * 5z * 12y + (12y)^2 = 25z^2 - 120zy + 144y^2$

- $(12z + 5y)^2 = (12z)^2 + 2 * 12z * 5y + (5y)^2 = 144z^2 + 120zy + 25y^2$

2. Add the two expanded expressions:

$$25z^2 - 120zy + 144y^2 + 144z^2 + 120zy + 25y^2$$

Combine like terms:

- $25z^2 + 144z^2 = 169z^2$

- $-120zy + 120zy = 0$

- $144y^2 + 25y^2 = 169y^2$

So, sum is:

$$169z^2 + 169y^2$$

3. Now subtract $144z^2$:

$$169z^2 + 169y^2 - 144z^2 = (169 - 144)z^2 + 169y^2 = 25z^2 + 169y^2$$

**Answer:** $25z^2 + 169y^2$

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