36*x^2-20*y^2/3*x+7*y find the quotient
To find the quotient of the expression 36*x^2 - 20*y^2 divided by 3*x + 7*y, we can use polynomial long division. Here's how you can do it step by step:
1. Write the dividend (36*x^2 - 20*y^2) and the divisor (3*x + 7*y) in long division format.
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3*x + 7*y | 36*x^2 - 20*y^2
2. Identify the first term of the dividend (36*x^2) and divide it by the first term of the divisor (3*x) to get 12*x.
12*x
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3*x + 7*y | 36*x^2 - 20*y^2
3. Multiply the result (12*x) by the divisor, and write the product below the dividend.
12*x*(3*x + 7*y)
36*x^2 + 84*x*y
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3*x + 7*y | 36*x^2 - 20*y^2
4. Subtract the product (36*x^2 + 84*x*y) from the dividend (36*x^2 - 20*y^2), and write the result below.
12*x*(3*x + 7*y)
- (36*x^2 + 84*x*y)
36*x^2 - 20*y^2
- (36*x^2 + 84*x*y)
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3*x + 7*y | -104*x*y - 20*y^2
5. Move on to the next term of the dividend (-104*x*y) and repeat steps 2-4.
6. Divide -104*x*y by 3*x to get -104/3*y.
12*x*(3*x + 7*y) - 104/3*y
- (36*x^2 + 84*x*y)
36*x^2 - 20*y^2
- (36*x^2 + 84*x*y)
_____________________
3*x + 7*y | -104*x*y - 20*y^2
-104/3*y
7. Multiply the result (-104/3*y) by the divisor, and write the product below.
12*x*(3*x + 7*y) - 104/3*y*(3*x + 7*y)
36*x^2 + 84*x*y
- (36*x^2 + 84*x*y)
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3*x + 7*y | -104*x*y - 20*y^2
-104/3*y
- (104/3*y^2 + 364/3*y)
8. Subtract the product (36*x^2 + 84*x*y) from the intermediate result (-104*x*y - 20*y^2), and write the result below.
12*x*(3*x + 7*y) - 104/3*y*(3*x + 7*y)
- (36*x^2 + 84*x*y)
36*x^2 - 20*y^2
- (36*x^2 + 84*x*y)
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3*x + 7*y | -104*x*y - 20*y^2 - 104/3*y^2 - 364/3*y
-104/3*y
- (104/3*y^2 + 364/3*y)
9. The resulting expression (-104*x*y - 20*y^2 - 104/3*y^2 - 364/3*y) is the quotient. Simplify it if necessary.
Therefore, the quotient of 36*x^2 - 20*y^2 divided by 3*x + 7*y is:
-104*x*y - 20*y^2 - 104/3*y^2 - 364/3*y