Question 895120: Can someone help me with these two questions
1. (4a-b)^4
2. 3/x+1=5/4
Thank you in advance
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your first problem involves the binomial expansion.
the binomial expansion formula says:
(x+y)^4 = 4c0*x^4*y^0
+ 4c1*x^3*y^1
+ 4c2*x^2*y^2
+ 4c3*x^1*y^3
+ 4c4*x^0*y^4
all you do is replace x with (4a) and y with (-b) and you have your solution.
you need to also know that:
4c0 = 1
4c1 = 4
4c2 = 6
4c3 = 4
4c4 = 1
that's the combination formula of nCx = n! / (x!*(n-x)!)
when all is said and done, you should get:
256*a^4 - 256*a^3*b + 96*a^2*b^2 - 16*a*b^3 + b^4
this answer has been confirmed by allowing a to be equal to 2 and b to be equal to 3 and solving the original equation and the final equation using my calculator.
both equations yielded 625 si i can assume the solution is good.
your second problem is, i believe:
3/(x+1) = 5/4
you need the parentheses to show that 3 is being divided by (x+1), rather than 3 is being divided by x and then 1 is added.
since i'm really not sure what you want, i'll do it both ways.
start with 3/(x+1) = 5/4
multiply both sides of the equation by 4/5 to get:
3*(4/5)/(x+1) = 1
multiply both sides of the equation by (x+1) to get:
3*(4/5) = x+1
subtract 1 from both sides to get:
3*(4/5)-1 = x
simplify to get:
x = 7/5
assuming your problem was:
(3/x) + 1 = 4/5, then you would do the following:
start with:
(3/x) + 1 = 4/5
subtract 1 from both sides of the equation to get:
3/x = 4/5 - 1
simplify to get:
3/x = -1/5
multiply both sides by x and multiply both sides by -5/1 to get:
3*(-5/1) = x
simplify to get:
-15 = x which is the same as x = -15.
both solutions have been confirmed to be good by replacing x with its solved for value from each equation.
that would be x = 7/5 in the first equation of 3/(x+1) = 4/5 and x = -15 in the second equation of (3/x) + 1 = 4/5.
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