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Solutions To Math Problem

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Mathematics
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Solve (2x 3y
4
)
3
(x
3
+ y)
0
(4xy 2)
3
The first thing to realize is that the expression (x
3
+ y)
0
= 1. This is because if you have any expression that has
an exponent of 0, it will be equal to 1. (So, for example, 3
0
and (x-1)
0
are both equal to 1).
So, the equation becomes: (2x 3y
4
)
3
(4xy 2)
3
We can rewrite this as: (2x 3y
4
)(2x 3y
4
)(2x 3y
4
)
(4xy 2) (4xy 2) (4xy 2)
To simplify this expression, we use the distributive property. Start by multiplying the first 2 expressions in the
numerator.
(2x 3y
4
)(2x 3y
4
) = (2x*2x) + (2x * -3y
4
) + (-3y
4
* 2x) + (-3y
4
*-3y
4
)
= 4x 6xy
4
6xy
4
+ 9y
8
= 4x 12xy
4
+ 9y
8
Do the same for the first 2 expressions in the denominator.
(4xy 2) (4xy 2) = (4xy*4xy) + (4xy* -2) + (-2 * 4xy) + (-2 * -2)
= 16x
2
y
2
8xy 8xy + 4
= 16 x
2
y
2
- 16xy + 4
The total equation now becomes:
(4x 12xy
4
+ 9y
8
) (2x 3y
4
)
(16x
2
y
2
16xy + 4) (4xy 2)
Multiply out the 2 equations in the denominator.
(4x 12xy
4
+ 9y
8
) (2x 3y
4
) = (4x*2x) + (-12xy
4
* 2x) + (9y
8
* 2x) + (4x * -3y
4
) +
(-12xy
4
* -3y
4
) + (9y
8
* -3y
4
)
= 8x
2
24x
2
y
4
+ 18xy
8
12x
2
y
4
+ 36xy
8
27y
12
= 8x
3
36x
2
y
4
+ 52xy
8
27y
12
Do the same for the 2 equations in the numerator.
(16x
2
y
2
16xy + 4)(4xy 2) = (16x
2
y
2
*4xy) + ( 16xy * 4xy) + (4 * 4xy) + (16x
2
y
2
*2) +
(16xy *2) + (4*2)
= 64x
3
y
3
64x
2
y
2
+ 16xy 32x
2
y
2
32xy 8
= 64x
3
y
3
96x
2
y
2
16xy 8
Put the two together to get your answer:
= 8x
3
36x
2
y
4
+ 52xy
8
27y
12
64x
3
y
3
96x
2
y
2
16xy 8

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Solve (2x – 3y4)3 (x3 + y)0 (4xy – 2)3 The first thing to realize is that the expression (x3 + y)0 = 1. This is because if you have any expression that has an exponent of 0, it will be equal to 1. (So, for example, 30 and (x-1)0 are both equal to 1). So, the equation becomes: (2x – 3y4)3 (4 ...
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Anonymous
Awesome! Perfect study aid.

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