F.3 math factorization

👨🏻‍🏫 學術台數學

[匿名]

2011-10-23 10:46 am

can anyone tell me why (m+n)^2-2(m+n)(m-n)+(m-n)^2 is = 4n^2

回答 (2)

用戶10012

2011-10-23 3:06 pm

✔ 最佳答案

Let m + n = a and m - n = b.
The expression becomes a^2 - 2ab + b^2 = (a - b)^2
= [(m + n) - (m - n)]^2
= (m + n - m + n)^2
= (2n)^2
= 4n^2.

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[匿名]

2011-11-01 4:10 pm

Let m + n = A and m - n = B.
The expression becomes A^2 - 2AB + B^2 = (A - B)^2
= [(m + n) - (m - n)]^2
= (m + n - m + n)^2
= (2n)^2
= 4n^2.

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