To factor the expression \((a - b)z + 3(b - a)^2\), we can start by rewriting \((b - a)^2\):
\[ (b - a)^2 = (-(a - b))^2 = (a - b)^2 \]
This means \((b - a)^2\) can be expressed as \((a - b)^2\) because squaring a negative value gives a positive value. Therefore, the expression can be rewritten as:
\[ (a - b)z + 3(a - b)^2 \]
Next, we can factor out the common factor \((a - b)\):
\[ = (a - b)(z + 3(a - b)) \]
Thus, the factored form of the expression \((a - b)z + 3(b - a)^2\) is:
\[ (a - b)(z + 3(a - b)) \]
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