Essay. Show all work. Find the following quotient: 36x^2-49y^2
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6x+7y
factor the numerator first(difference of squares)
36x^2-49y^2 = (6x-7y)(6x+7y)
now you see (6x+7y) top and bottom so in the end the result is
6x-7y
To find the quotient, we need to divide the numerator by the denominator.
Step 1: Simplify the expression
36x^2 - 49y^2 is a difference of squares, so we can rewrite it as (6x)^2 - (7y)^2.
Step 2: Apply the difference of squares formula
The difference of squares formula states that a^2 - b^2 = (a + b)(a - b). We can apply this formula to simplify our expression further:
(6x)^2 - (7y)^2 = (6x + 7y)(6x - 7y).
Step 3: Divide numerator by denominator
Now that we have simplified our expression, we can proceed with dividing the numerator by the denominator:
(6x + 7y) / (6x + 7y) * (6x - 7y) / (6x + 7y).
Step 4: Cancel out the common factors
Notice that the (6x + 7y) term appears in both the numerator and denominator, so we can cancel it out:
= (6x - 7y) / 1.
Step 5: Simplify the final expression
Since any number divided by 1 is itself, our final quotient is:
6x - 7y.