FACTORISE 4(a-b)^2-4
I already made it into 4a^2-8ab+4b^2-4
but what is next?
PLEASE I NEED A MATH TEAHCER!HOW DO I FACTORISE 4(a-b)^2-4?
2008-09-14 6:59 am
回答 (8)
2008-09-14 7:05 am
✔ 最佳答案
Take 4 out as a factor:4[((a-b)^2)-1)]
this is a difference of two squares, so you get:
4[(a-b-1)(a-b+1)]
2008-09-14 7:10 am
1st factor is 4:
4(a - b)² - 4 = 0
4(a - b)² = 4
(a - b)² = 1
2nd & 3rd factor
(a - b)² - 1 = 0
(a - b + 1)(a - b - 1) = 0
Answer: 4(a - b + 1)(a - b - 1) are the factors.
Proof:
Original expression = Factored expression
4(a - b)² + 4 = 4(a - b + 1)(a - b - 1)
4(a² - ab - ab + b²) + 4 = 4(a² - ab - a - ab + b² - b + a + b - 1)
4(a² - 2ab + b²) - 4 = 4(a² - 2ab + b² - 1)
4a² - 8ab + 4b² - 4 = 4a² - 8ab + 4b² - 4
4(a - b)² - 4 = 0
4(a - b)² = 4
(a - b)² = 1
2nd & 3rd factor
(a - b)² - 1 = 0
(a - b + 1)(a - b - 1) = 0
Answer: 4(a - b + 1)(a - b - 1) are the factors.
Proof:
Original expression = Factored expression
4(a - b)² + 4 = 4(a - b + 1)(a - b - 1)
4(a² - ab - ab + b²) + 4 = 4(a² - ab - a - ab + b² - b + a + b - 1)
4(a² - 2ab + b²) - 4 = 4(a² - 2ab + b² - 1)
4a² - 8ab + 4b² - 4 = 4a² - 8ab + 4b² - 4
2008-09-14 7:03 am
4(a-b)^2-4
This is a difference of two perfect squares.
x^2-y^2 = (x+y)(x-y)
so
4(a-b)^2-4
(2(a-b) + 2)(2(a-b) - 2)
Do you see it now?
This is a difference of two perfect squares.
x^2-y^2 = (x+y)(x-y)
so
4(a-b)^2-4
(2(a-b) + 2)(2(a-b) - 2)
Do you see it now?
2008-09-14 7:02 am
you do not need to expand
take 4 common
4[(a-b)2^-1]
1 is 1^2
so 4[(a-b)2^-1^2]
= 4(a-b +1)(a-b-1) as of the form x^2 - y^2
take 4 common
4[(a-b)2^-1]
1 is 1^2
so 4[(a-b)2^-1^2]
= 4(a-b +1)(a-b-1) as of the form x^2 - y^2
2008-09-14 10:05 am
4(a - b)^2 - 4
= (2^2)(a - b)^2 - 2^2
= [2(a - b) + 2][2(a - b) - 2]
= [2a - 2b + 2][2a - 2b - 2]
= 4[a - b + 1][a - b - 1]
= (2^2)(a - b)^2 - 2^2
= [2(a - b) + 2][2(a - b) - 2]
= [2a - 2b + 2][2a - 2b - 2]
= 4[a - b + 1][a - b - 1]
2008-09-14 7:03 am
[4(a-b)^2 -4)]
= [2(a-b) - 2][2(a-b) + 2]
= [2(a-b) - 2][2(a-b) + 2]
2008-09-14 7:03 am
Expanding it is probably the wrong way to do it.
Think about the difference of two squares:
(x^2 - y^2) = (x + y)(x - y)
Compare it to what you have. See a similarity?
Think about the difference of two squares:
(x^2 - y^2) = (x + y)(x - y)
Compare it to what you have. See a similarity?
2008-09-14 7:02 am
4(a-b)^2 - 4
= 4{(a-b)^2 - 1}
= 4{(a-b)^2 - 1^2}
= 4(a-b+1)(a-b-1)
Ans: 4(a-b+1)(a-b-1)
= 4{(a-b)^2 - 1}
= 4{(a-b)^2 - 1^2}
= 4(a-b+1)(a-b-1)
Ans: 4(a-b+1)(a-b-1)
收錄日期: 2021-05-01 11:10:59
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080913225902AA8YJSu