Essay. Show all work. Find the quotient.

49a^2-b^2
---------
7a-b

factor the numerator, it is a difference of squares

please get into more detail more for me to understand Algebra is one my weakest subjects

These sites will help you understand this problem and its solution.

http://www.purplemath.com/modules/factquad.htm

http://www.purplemath.com/modules/specfact.htm

http://www.youtube.com/watch?v=wvFr1BqU4g8

plz help me

Here is an example:

9x^2 - 25y^2
------------
3x - 5y

Factor the numerator, its a difference of perfect squares.

9x^2 - 25y^2 = (3x - 5y) (3x + 5y)

(3x - 5y)(3x + 5y)

(3x)(3x) = 9x^2

(3x)(5y) = 15xy

(-5y)(3x)= -15xy

(-5y)(5y)= -25y^2

9x^2 + 15xy - 15xy -25y^2

9x^2 -25y^2 = (3x - 5y)(3x + 5y)
---------------------------------

9x^2 - 25y (3x - 5y)(3x +5y)
---------- = ---------------- = 3x +5y
3x - 5y 3x - 5y

To find the quotient of the given expression, 49a^2 - b^2 divided by 7a - b, we can use the concept of polynomial long division. Here's how to do it step by step:

Step 1: Arrange the dividend and divisor in long division form:
___________________
7a - b | 49a^2 - b^2

Step 2: Divide the first term of the dividend by the first term of the divisor. In this case, divide 49a^2 by 7a, which gives us 7a.

7a
___________________
7a - b | 49a^2 - b^2

Step 3: Multiply the divisor (7a - b) by the quotient obtained in the previous step.
Multiplying, we get: (7a - b)(7a) = 49a^2 - 7ab

7a
___________________
7a - b | 49a^2 - b^2
- (49a^2 - 7ab)
___________________

Step 4: Subtract the result obtained in the previous step from the original dividend.
Subtracting, we get: (49a^2 - b^2) - (49a^2 - 7ab) = - b^2 + 7ab

7a
___________________
7a - b | 49a^2 - b^2
- (49a^2 - 7ab)
___________________
- b^2 + 7ab

Step 5: Now, we have a new expression (-b^2 + 7ab) which needs to be divided by the original divisor (7a - b). Repeat steps 2-4 with this new expression:

Divide the first term of the new expression (-b^2 + 7ab) by the first term of the divisor (7a - b). In this case, divide -b^2 by 7a, which gives us -1/7.

7a - 1/7
___________________
7a - b | 49a^2 - b^2
- (49a^2 - 7ab)
___________________
- b^2 + 7ab

Step 6: Multiply the divisor (7a - b) by the new quotient obtained in the previous step.
Multiplying, we get: (7a - b)(-1/7) = -a + b/7

7a - 1/7
___________________
7a - b | 49a^2 - b^2
- (49a^2 - 7ab)
___________________
- b^2 + 7ab
- ( -a + b/7)
___________________

Step 7: Subtract the result obtained in the previous step from the previous remainder (- b^2 + 7ab).
Subtracting, we get: (-b^2 + 7ab) - (-a + b/7) = - b^2 + 7ab + a - b/7

7a - 1/7
___________________
7a - b | 49a^2 - b^2
- (49a^2 - 7ab)
___________________
- b^2 + 7ab
- ( -a + b/7)
___________________
- b^2 + 7ab + a - b/7

Step 8: Since there are no more terms to divide, the division is complete.

Therefore, the quotient of 49a^2 - b^2 divided by 7a - b is:
7a - 1/7 + (- b^2 + 7ab + a - b/7) / (7a - b)