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Step 1:I'll solve this step by step, carefully following the LaTeX formatting guidelines:
Step 2:: Expand the first term 3(x- 2)^{2}
- Multiply by $$3$$: $$3(x-2)^{2} = 3x^{2} - 12x + 12
- First, expand (x- 2)^{2} using the square of a binomial formula: a^{2} = a \cdot a
Step 3:: Expand the second term - 2(x- 1)
- Distribute $$-2$$ to $$(x-1)
- - 2(x- 1) = - 2x + 2
Step 4:: Combine the expanded terms
- $$= 3x^{2} - 12x + 12 - 2x + 2
- Add the results from Step 1 and Step 2
Step 5:: Simplify by combining like terms
- Combine the linear terms: $$-12x - 2x = -14x
- Combine the constant terms: 12 + 2 = 14
Final Answer
3x^{2} - 14x + 14
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