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tmlfan_179027
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How would you factor 8x^6+64? My text states that the answer is 8(x^2+2)(x^4-2x^2+4). How would you get to that?
Factoring is the process of breaking down a mathematical expression into smaller parts that can be multiplied together to get the original expression. It is important in mathematics because it allows us to simplify complex expressions and solve equations more easily.
The first step is to identify the common factor among all the terms in the expression. Then, divide each term by the common factor and write the result in parenthesis. This common factor can then be factored out, leaving behind the remaining terms.
Yes, you can factor an expression with variables and exponents. The key is to use the rules of exponents to rewrite the expression in a form where the common factor can be identified and factored out.
The first step is to identify the common factor, which in this case is 8. We can rewrite the expression as 8(x^6+8). Then, we can further factor the expression inside the parenthesis using the rule of a^3+b^3=(a+b)(a^2-ab+b^2). The final factored form is 8(x^2+2x+4)(x^4-2x^3+4x^2-8x+16).
Yes, the expression 8x^6+64 can be factored further. We can use the rule of a^2+b^2=(a+b)(a-b) to factor the quadratic expression inside the parenthesis. The final factored form is 8(x^2+2x+4)(x^2-2x+4)(x^2+4).