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Answer :
Certainly! Let's break down the expression [tex]\( x^4 + 625y^4 \)[/tex] step-by-step.
1. Analyze the Expression:
- The given expression is [tex]\( x^4 + 625y^4 \)[/tex].
- Notice that [tex]\( 625y^4 \)[/tex] can be rewritten using powers of 5: [tex]\( 625 = 5^4 \)[/tex], so [tex]\( 625y^4 = (5^2)^2 \cdot y^4 = (5y^2)^2 \)[/tex].
2. Identify Factoring Techniques:
- Typically, when dealing with expressions like [tex]\( a^4 + b^4 \)[/tex], there are no straightforward factorizations over the real numbers. This is because it involves a sum of two fourth powers which is not factorable into simpler real polynomial terms in general form.
- We could factor it using complex numbers, but that may not be required often.
3. Conclusion on Simplification:
- Therefore the given expression [tex]\( x^4 + 625y^4 \)[/tex] doesn't simplify further using standard algebraic techniques over the real numbers.
So, in conclusion, the expression [tex]\( x^4 + 625y^4 \)[/tex] remains as it is:
[tex]\[ x^4 + 625y^4 \][/tex]
1. Analyze the Expression:
- The given expression is [tex]\( x^4 + 625y^4 \)[/tex].
- Notice that [tex]\( 625y^4 \)[/tex] can be rewritten using powers of 5: [tex]\( 625 = 5^4 \)[/tex], so [tex]\( 625y^4 = (5^2)^2 \cdot y^4 = (5y^2)^2 \)[/tex].
2. Identify Factoring Techniques:
- Typically, when dealing with expressions like [tex]\( a^4 + b^4 \)[/tex], there are no straightforward factorizations over the real numbers. This is because it involves a sum of two fourth powers which is not factorable into simpler real polynomial terms in general form.
- We could factor it using complex numbers, but that may not be required often.
3. Conclusion on Simplification:
- Therefore the given expression [tex]\( x^4 + 625y^4 \)[/tex] doesn't simplify further using standard algebraic techniques over the real numbers.
So, in conclusion, the expression [tex]\( x^4 + 625y^4 \)[/tex] remains as it is:
[tex]\[ x^4 + 625y^4 \][/tex]
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Rewritten by : Jeany
