There are a few problems on my homework im having trouble on. can you explain how to do these problems? thanks
1. x^2+10x+25-9y^2
2. x^2+2x-3
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x^2+3x--2
3. 2xSQRT(x^2+5) - 2x^3/x^2+5
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x^2+5
sorry #3 is kinda big. and gave me most trouble, #2 might actually be really easy but im probably overthinking it.
You do not say what to. Factor, reduce?
x^2+10x+25-9y^2
= (x+5)^2 - 9 y^2
so what?
if it were equal to something it might be a hyperbola :)
x^2+2x-3
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x^2+3x+2
= [(x+3)(x-1)] / [(x+2)(x+1)]
2xSQRT(x^2+5) - 2x^3/(x^2+5)
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(x^2+5)
2x [ SQRT(x^2+5) - x^2/(x^2+5)]
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(x^2+5)
2x [ (x^2+5)^1.5 - x^2]
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(x^2+5)
not much I see to do
1. x^2 + 10x + 25 - 9y^2.
x^2 + 10x + 25 is a perfect square:
(x+5)^2 - 9y^2. The difference of two squares.
((x+5) + 3y) * ((x+5)-3y).
2. x^2 + 2x - 3. Factor it:
(x+3)(x-1).
Of course! I'll walk you through each problem step by step.
1. x^2+10x+25-9y^2:
To simplify this expression, first look for any like terms that can be combined. In this case, we have terms with x^2, x, and constants.
The expression becomes: (x^2 + 10x) + (25 - 9y^2)
Now, let's factor the trinomial x^2 + 10x. We can rewrite it as (x + 5)(x + 5), which is equal to (x + 5)^2.
The expression now becomes: (x + 5)^2 + (25 - 9y^2)
2. (x^2+2x-3) divided by (x^2+3x-2):
To simplify this division, we can either factor both the numerator and denominator or use polynomial long division. Let's factor them:
The numerator can be factored as (x - 1)(x + 3).
The denominator can be factored as (x - 1)(x + 2).
Now, we cancel out the (x - 1) factor in both the numerator and denominator:
(x - 1)/(x + 2)
3. (2x√(x^2+5) - 2x^3)/(x^2+5):
This expression seems complex, but we can simplify it step by step.
First, factor out the common factor of 2x from the numerator:
2x(√(x^2+5) - x^2) / (x^2+5)
Next, let's simplify the denominator. It's already in its simplest form.
Now, let's work on the square root in the numerator: √(x^2+5).
Since we can't simplify it further, we leave it as it is.
Finally, let's combine all the simplified terms:
(2x(√(x^2+5) - x^2)) / (x^2+5)
That's it! I hope this explanation helps. If you have any further questions, feel free to ask!