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3. 下列选项中不能运用平方差公式的有（） A. (a+b+c)(a−b+c)(a+b+c)(a-b+c) B. (a−b+c)(−a+b−c)(a-b+c)(-a+b-c) C. $(a-b+c)(a+...
Mar 17, 2024
3. 下列选项中不能运用平方差公式的有（） A. (a+b+c)(a−b+c)(a+b+c)(a-b+c) B. (a−b+c)(−a+b−c)(a-b+c)(-a+b-c) C. (a−b+c)(a+b−c)(a-b+c)(a+b-c) D. (−a+b+c)(−a−b−c)(-a+b+c)(-a-b-c)
Solution by Steps
step 2
Examine option A: (a+b+c)(a−b+c) (a+b+c)(a-b+c) expands to a2+2ac−b2+c2 a^2 + 2ac - b^2 + c^2 , which does not fit the difference of squares formula
step 3
Examine option B: (a−b+c)(−a+b−c) (a-b+c)(-a+b-c) expands to −a2+2ab−2ac−b2+2bc−c2 -a^2 + 2ab - 2ac - b^2 + 2bc - c^2 , which does not fit the difference of squares formula
step 4
Examine option C: (a−b+c)(a+b−c) (a-b+c)(a+b-c) expands to a2−b2+2bc−c2 a^2 - b^2 + 2bc - c^2 , which does not fit the difference of squares formula
step 5
Examine option D: (−a+b+c)(−a−b−c) (-a+b+c)(-a-b-c) expands to a2−b2−2bc−c2 a^2 - b^2 - 2bc - c^2 , which does not fit the difference of squares formula
A
Key Concept
Difference of Squares
Explanation
The difference of squares formula applies to expressions that can be written in the form (x+y)(x−y) (x+y)(x-y) , resulting in x2−y2 x^2 - y^2 . None of the given options can be directly expressed in this form after expansion.
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