please show me step by step
2007-09-05 08:59:53 · 6 answers · asked by AnswerGirl 2 in Science & Mathematics ➔ Mathematics
Difference of squares. Basically you take the square root.
First start with 25x².
What times what will give you 25? 5.
What times what will give you x²? x.
So (5x)(5x) = 25x²
(5x + ?)(5x - ?) = 25x² - y²
Now you have the -y².
What times what will give you -y²: *Negative
Because it's squared .. the answer is y.
Because it's negative.. one has to be a positive and the other a negative.
So you had:
(5x)(5x) = 25x²
Now add the +y and -y in the brackets.
(5x + y)(5x - y) = 25x² - y²
Proof: Foil it out.
(5x+y)(5x-y)=
25x² -5xy + 5xy - y²
= 25x² - y²
2007-09-05 09:14:30 · answer #1 · answered by Anonymous · 0⤊ 0⤋
(a^2-b^2) is the difference of two squares, and its factors are (a+b)(a-b).
(25x^2-y^2) is also the difference of two squares, so it follows the same pattern: (5x+y)(5x-y)
There is no step by step procedure. You just have to know that if a binomial consists of two perfect squares with a - sign between the two terms, the factors are
(rt 1st term+rt 2nd term)(rt 1st term-rt 2nd term)
If we work backwards, you will see why this is so.
FOIL (5x+y)(5x-y)=25x^2 -5xy+5xy-y^2
which gives 25x^2-y^2
2007-09-05 16:15:43 · answer #2 · answered by Grampedo 7 · 0⤊ 0⤋
This is an example of a "difference of squares"
The rule is: x^2 - y^2 = (x-y)(x+y)
In this case, you almost have the exact same thing, except that the first term isn't the square of x.. it's the square of ???
2007-09-05 16:08:18 · answer #3 · answered by Yokki 4 · 0⤊ 0⤋
(5x-y)(5x+y)
You should remember a^2 -b^2 = (a-b)(a+b)
2007-09-05 16:08:39 · answer #4 · answered by ironduke8159 7 · 0⤊ 0⤋
difference of two squares:
(5x+y)(5x - y)
2007-09-05 16:06:24 · answer #5 · answered by John V 6 · 0⤊ 0⤋
25x²-y² =(5x-y)(5x+y)
2007-09-05 16:09:35 · answer #6 · answered by Anonymous · 0⤊ 0⤋