You can factor this as a sum of cubes.appplejack said:Homework Statement
I need to factor the following.
8x^6+64?
Homework Equations
The Attempt at a Solution
I really have no idea. I can pull 8 out and write 8(x^6)+64 but it doesn't get father than that.
If you're going to do that, pull out 8 from both terms.appplejack said:I can pull 8 out and write 8(x^6)+64 but it doesn't get father than that.
The GCF of the terms in the expression can be found by identifying the factors of each term and selecting the largest factor that is common to all terms. In this case, the GCF would be 8x^6 since it is a factor of both terms.
To factor out the GCF, divide each term by the GCF and write it outside of the parentheses. In this case, the expression would become 8x^6(1+8).
Yes, the expression can be factored further by using techniques such as grouping, difference of squares, and trinomial factoring. However, in this case, the expression cannot be factored any further.
You can check by multiplying the factors together and verifying that it results in the original expression. In this case, 8x^6(1+8) would result in 8x^6+64, confirming that the factored expression is correct.
Factoring expressions is useful in solving equations, simplifying algebraic expressions, and understanding patterns in data. It is also used in fields such as engineering, computer science, and economics to solve real-world problems and make predictions.