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Dima020 [189]
3 years ago
6

Expand the equation (2x+3)^4

Mathematics
1 answer:
inysia [295]3 years ago
6 0
(2x+3)(2x+3)(2x+3)(2x+3)
(4x^2+12x+9)(4x^2+12x+9)
16x^4+48x^3+36x^2+48x^3+144x^2+108x+36x^2+108x+81
16x^4+(48+48)x^3+(36+144+36)x^2+(108+108)x+81

ans:  16x^4+96x^3+216x^2+216x+81
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The numerator of a fraction (which is in its simplest form) is 5 less than the denominator. If the numerator is multiplied by 2,
timama [110]
N = d - 5

2n/(d + 16) = n/d - 1/3 n/d
2n/(d + 16) = 2/3 n/d Divide by 2n
1 / (d + 16) = 1/3 d
Here's the tricky part.
d + 16 = 3d the two denominators are equal. the numerators are both 1.
16 = 2d
d = 8
so the numerator is d - 5
n = 8 - 5
n = 3

Let's see if it checks out.
n = 3
d = 8

2*3 = 6
8 + 16 = 24
New fraction 6/24 = 1/4
(3/8 - 1/3 ) = 1/8
3/8 - 1/8 = 1/4 so it checks with the original conditions put on it.


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Answer: 5/13

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