36x^2 - 49y^2 divided by 6x + 7y
meaning 36x^2 - 49y^2 is on top and
6x + 7y is on bottom.
Please help, my teacher nor course book covers when there are different variables
Jai,
Oh my gosh, thank you so much. I even understand exactly how you go the answer. I've been doing the tutoring at my school for almost 2 days with the same tutor and they cannot explain it on an easy to understand level. I really really appreciate your help!!!!!
you're welcome, Jordyn! :)
To divide the expression (36x^2 - 49y^2) by (6x + 7y), you can use the method of polynomial long division. Here are the steps to follow:
Step 1: Arrange the terms of the dividend and the divisor in descending powers of x.
Dividend: 36x^2 - 49y^2
Divisor: 6x + 7y
Step 2: Divide the first term of the dividend (36x^2) by the first term of the divisor (6x) to get the quotient's first term.
Quotient's first term = (36x^2 / 6x) = 6x
Step 3: Multiply the divisor (6x + 7y) by the quotient's first term (6x), and subtract the result from the dividend.
(36x^2 - 49y^2) - (6x * (6x + 7y))
Simplify the expression:
36x^2 - 49y^2 - 36x * 6x - 36x * 7y
Step 4: Continue dividing the remaining terms following the same process as step 2.
- Multiply the quotient's first term (6x) by the divisor (6x + 7y).
- Subtract the result from the previous step from the remaining terms of the dividend.
Repeat these steps until you have evaluated all the terms.
Step 5: Simplify the expression obtained from the previous step by combining like terms.
Step 6: Write the final answer, noting any remainder if it exists.
The final answer will be in the form of:
Quotient + (Remainder / Divisor)
(36x^2 - 49y^2)/(6x + 7y)
notice that the numerator is a difference of two squares,, recall:
a^2 - b^2 = (a+b)(a-b)
thus the numerator can be factored into:
(6x+7y)(6x-7y)/(6x+7y)
then cancel the common factor and you get 6x - 7y
hope this helps.