# Tagged Questions

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### Basic Algebraic Manipulation

How would I solve for $X$ in this instance? I can't figure out how to get the $X$ variables by themselves and the known values on the other side by themselves. $2(4-X)(4-X)+X = 3$
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### Factor this equation [closed]

Can someone factor this for me? $(x^{\frac{n}3}-a^{\frac{n}3})$ I am stuck on it. Let n be any natural number.
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### Is this factorization true for all $n$ in the natural numbers

I need to know if $x-a=(x^{\frac{n}3}-a^{\frac{n}3})(x^{\frac{n+1}3}+a^{\frac{n}3} x^{\frac{n}3}+a^{\frac{n+1}3})$ Is true. I know its true for $n=1$, is it true for all natural numbers though?
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### What is the solution? Factoring and computing the equation.

If you will be gracious enough to answer, the equation is currently: $$10^x + 15^{x-1}= 20,$$ What is the value of $2x^2$? Please list all steps, if you don't mind. To follow up, what is the name of ...
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### Factorization of a degree three polynomial

So I was doing some Vector Calculus homework and was working with Lagrange Multipliers, but then I came across a polynomial that I either forgot how to factor or never learned. I plugged it into ...
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### Factorise: $a^4-b^4+c^4-d^4-2(a^2c^2-b^2d^2)+4ac(b^2+d^2)-4bd(a^2+c^2)$

Factorise: $a^4-b^4+c^4-d^4-2(a^2c^2-b^2d^2)+4ac(b^2+d^2)-4bd(a^2+c^2)$. My working: $(a^4-2a^2c^2+c^4)-(b^4-2b^2d^2+d^4)+4ac(b^2+d^2)-4bd(a^2+c^2)$ ...
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### Solve $t^4+4 t^3+6 t^2+4 t-32 t^{1/4}+1 = -16$

I'm trying to solve the following equation: $$(t+1)^4 - 32 t^{\frac{1}{4}}=-16$$ where t $\geq 0$, which is equivalent to $$t^4+4 t^3+6 t^2+4 t-32 t^{\frac{1}{4}}+1 = -16$$ Wolfram Alpha tells that ...
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### What is the line of thinking to get $[(n^2+3n+1)^2-5n(n+1)^2]$ from $(n^4+n^3+n^2+n+1)$?

There is this one little tiny step along the working that I don't quite understand, but I think it is better if I write the whole problem and solution for clarity. Problem: Factorise $5^{1995}-1$ ...
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### Substitution to linear + nth power form

Given an arbitrary polynomial: $$a_0 + a_1x + a_2x^2 ... a_nx^n$$ Does there exist a series of substitutions (or single substitution if you choose to combine them) that leaves this function in the ...
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### how do you find the highest common factor of two multivariate polynomials?

How do you find the highest common factor of two multivariate polynomials? I am happy to get answers that are only useful for polynomials over the real numbers, as that is what I am dealing with.
I'm currently doing some homework, but I'm COMPLETELY stuck on one problem. I need to factor the following trinomial: $$5x^2+7xy+2y^2$$ How can I solve this problem? I have no idea what to do ...
can anyone explain me how to isolate the j variable please? $$q = \frac{1 - (1 + j)^{-n}}{j} p$$ TIA