- #1

MorallyObtuse

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## Homework Statement

Express as the product of four factors

Is this correct?

[tex]a^6 - b^6 = (a - b)(a^5 + a^4b + a^3b^2 + a^2b^3 + ab^4 + b^3)[/tex]

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In summary: Then you should talk to your teacher about it.I did get it, just joking with 1/2" :biggrin:And thanks very much :)

- #1

MorallyObtuse

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Express as the product of four factors

Is this correct?

[tex]a^6 - b^6 = (a - b)(a^5 + a^4b + a^3b^2 + a^2b^3 + ab^4 + b^3)[/tex]

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- #2

HallsofIvy

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What you have written isMorallyObtuse said:## Homework Statement

Express as the product of four factors

Is this correct?

[tex]a^6 - b^6 = (a - b)(a^5 + a^4b + a^3b^2 + a^2b^3 + ab^4 + b^3)[/tex]

- #3

MorallyObtuse

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I don't get it?!

- #4

1/2"

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By the law of indices (a

and so you can also represent it like this(like HallsofIvy said)

=(a^3)^2-(b^3)^2

And then you can simplyfy it like this

=(a^3-b^3)(a^3+b^3)

and finaly u have your 4 terms

(a-b) (a^2+ab+b^2) (a+b)(a^2-ab+b^2)

I think you get it.

- #5

MorallyObtuse

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1/2" said:

By the law of indices (a^{m})^{n}=a^{mxn}

and so you can also represent it like this(like HallsofIvy said)

=(a^3)^2-(b^3)^2

And then you can simplyfy it like this

=(a^3-b^3)(a^3+b^3)

and finaly u have your 4 terms

(a-b) (a^2+ab+b^2) (a+b)(a^2-ab+b^2)

I think you get it.

No I don't get it

- #6

Mark44

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Each factor on the right can be further factored using known formulas for the sum of cubes and difference of cubes.

- #7

HallsofIvy

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MorallyObtuse said:I don't get it?!

Then you should talk to your teacher about it.MorallyObtuse said:No I don't get it

- #8

MorallyObtuse

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I did get it, just joking with 1/2"

- #9

MorallyObtuse

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And thanks very much :)

[itex](a-b) (a^2+ab+b^2) (a+b)(a^2-ab+b^2)[/itex]

[itex](a-b) (a^2+ab+b^2) (a+b)(a^2-ab+b^2)[/itex]

- #10

Borek

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[tex]1 \times 1 \times 1 \times (a^6 - b^6)[/tex]

- #11

Mark44

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[tex]1 \times 1 \times 1 \times 1 \times 1 \times 1 \times (a^6 - b^6)[/tex]

- #12

HallsofIvy

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- #13

Mark44

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I was hoping for extra credit because I went above and beyond the requirements.

When we express a number as the product of four factors, we are breaking down the number into four smaller numbers that, when multiplied together, equal the original number. This can also be thought of as finding the prime factorization of a number.

Expressing a number as the product of four factors can help us understand the factors and factors of factors that make up a number. This can be useful in many areas of math, such as finding common factors or simplifying fractions.

To find the factors of a number, we can start by listing all of the possible factors and then narrowing down the list by testing each factor to see if it divides evenly into the original number. Another method is to use prime factorization, where we find the prime factors of a number and then combine them to find all of the factors.

Yes, every number can be expressed as the product of four factors. This is because every number can be broken down into prime factors, and we can combine these prime factors to create four factors that equal the original number.

We can use the product of four factors to solve equations by breaking down the numbers in the equation into their prime factors and then rearranging them to find the solution. This can be a useful method for solving equations with large numbers or multiple variables.

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