Factorization of a difference of 2 squares? ?

2008-11-27 9:10 am
16-25(a-3)2<e.i to the square>
更新1:

16-25(a-3)2<e.i to the square> The answer must be: -(19+5a)(11+5a) Its written in the answer sheet but i don't know how to work it.

回答 (3)

2008-11-27 10:36 am
✔ 最佳答案
a^2 - b^2 = (a + b)(a - b)

16 - 25(a - 3)^2
= 4^2 - 5^2(a - 3)^2
= 4^2 - [5(a - 3)^2]
= {4 + [5(a - 3)]}{4 - [5(a - 3)]}
= {4 + 5(a - 3)}{4 - 5(a - 3)}
= {4 + 5a - 15}{4 - 5a + 15}
= {5a - 15 + 4}{-5a + 4 + 15}
= {5a - 11}{-5a + 19}
2008-11-27 5:17 pm
a^2 - b^2 = (a-b)(a+b)

hence

16-25(a-3)^2 = (4 - 5[a-3])(4+5[a-3])
2008-11-27 7:27 pm
16 - 25(a - 3)²
( 4 - 5(a - 3) )(4 + 5 (a - 3) )
(19 - 5a) (- 11 + 5a)


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