MHB Can These Expressions Be Factored Correctly?

[mathdad]

Factor the following three questions.

1. 4u^2 + 25v^2

I say this one cannot be factored because the expression is irreducible over the integers.

Right?

2. (81/4) - y^2

Let (81/4) = (9/2)(9/2).

So, (81/4) - y^2 factors out to be (9/2 - y)(9/2 + y).

Right?

3. 8a^3 + 27b^3 + 2a + 3b

I must apply the sum of cubes to the expression 8a^3 + 27b^3 as a first step, right?

If so, then a = 2^3 and b = 3^3 in the sum of cubes, right?

I did not ask for the problems to be solved. I simply want to know if my work is correct or not. If it is wrong, make the corrections and allow me to do the math.

 

[Greg]

1. Correct.

2. Correct.

3. Yes, apply the sum of cubes formula to $8a^3+27b^3$. Be careful with your variable names. $a$ does not necessarily equal $2^3$. In another post you stated $a=(a+b)$. This is only true if $b=0$. Try choosing different letters for different variables. For example, you may be given to factor

$$125a^3-64b^3$$

Then write

$$p=5a$$ and $$q=4b$$

It makes no real difference what other letters you choose; these letters reflect given values no matter what they are.

It is entirely incorrect to state $a=5a$ and $b=4b$ in the context you are working in. At any rate, those two equations are only true if $a$ and $b$ are equal to $0$

Have you thought of learning $\LaTeX$? :)

 

[mathdad]

1. Correct.

2. Correct.

3. Yes, apply the sum of cubes formula to $8a^3+27b^3$. Be careful with your variable names. $a$ does not necessarily equal $2^3$. In another post you stated $a=(a+b)$. This is only true if $b=0$. Try choosing different letters for different variables. For example, you may be given to factor

$$125a^3-64b^3$$

Then write

$$p=5a$$ and $$q=4b$$

It makes no real difference what other letters you choose; these letters reflect given values no matter what they are.

It is entirely incorrect to state $a=5a$ and $b=4b$ in the context you are working in. At any rate, those two equations are only true if $a$ and $b$ are equal to $0$

Have you thought of learning $\LaTeX$? :)

I do not have a computer. No time to learn LaTex. I will try to post pictures of my work for easy reading. Thank you for your help.