To find the product of \((2 - 5z)^2\), we can use the formula for squaring a binomial, which is:
\[ (a - b)^2 = a^2 - 2ab + b^2 \]
In our case, \(a = 2\) and \(b = 5z\). Now we can apply the formula:
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Calculate \(a^2\): \[ a^2 = 2^2 = 4 \]
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Calculate \(2ab\): \[ 2ab = 2 \cdot 2 \cdot 5z = 20z \]
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Calculate \(b^2\): \[ b^2 = (5z)^2 = 25z^2 \]
Now we can write the expression using the values we calculated:
\[ (2 - 5z)^2 = a^2 - 2ab + b^2 = 4 - 20z + 25z^2 \]
Next, we arrange the expression in standard form (descending powers of \(z\)):
\[ 25z^2 - 20z + 4 \]
Thus, the product of \((2 - 5z)^2\) in standard form is:
\[ \boxed{25z^2 - 20z + 4} \]
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