Identities and factorize(F.2)

1).
28m² - 28m + 7
= 7(4m² - 4m + 1)
= 7[(2m) ² - 2(2m)(1) + (1)²]
= 7(2m - 1)²


2).
18 + 50a² + 60a
= 50a² + 60a + 18
= 2(25a² + 30a + 9)
= 2[(5a)² + 2(5a)(3) + (3)²]
= 2(5a + 3)²


3).
If it is (a + 1)² - 8(a + 1) + 16, put u = a + 1
Then, (a + 1)² - 8(a + 1) + 16
= u² - 8u + 16
= (u)² - 2(u)(4) + (4)²
= (u - 4)²
= [(a + 1) - 4]²
= (a - 3)²

If it is (a - 1)² - 8(a - 1) + 16, put u = a + 1
Then, (a - 1)² - 8(a - 1) + 16
= u² - 8u + 16
= (u)² - 2(u)(4) + (4)²
= (u - 4)²
= [(a - 1) - 4]²
= (a - 5)²

If it is (a + 1)² - 8(a - 1) + 16,
then (a + 1)² - 8(a - 1) + 16
= a² + 2a + 1 - 8a + 8 + 16
= a² - 6a + 25
It cannot be factorized.


4).
Put u = a + b
Then, (a + b)² - (a + b)²
= u² - u²
= 0


5).
Put u = x - y
Then, x² - 2xy + y² - 1
= (x² - 2xy + y²) - 1
= (x - y)² - 1
= u² - 1
= (u + 1)(u - 1)
= (x - y + 1)(x - y - 1)


6).
x⁴ - 16
= (x²)² - (4)²
= (x² + 4)(x² - 4)
= (x² + 4)(x² - 2²)
= (x² + 4)(x + 2)(x - 2)

2011-02-11 12:07:38 補充：
你還是檢查一下有沒有打錯題目吧。

2011-02-12 11:49:22 補充：
4.
Put u = a + b, and v = a - b

(a + b)² - (a - b)²
= u² - v²
=(u + v)(u - v)
= [(a + b) + (a - b)] [(a + b) - (a - b)]
= (a + b + a - b)(a + b - a + b)
= (2a)(2b)
= 4ab ...... (answer)

(a+b)^2-(a-b)^2
(a+b-a+b)(a+b+a-b)
2b*2a
4ab
_________________
(a+b)^2-(a-b)^2
a^2+2ab+b^2-a^2+2ab-b^2
4ab