Final answer:
the simplified expression for h=√(m²-n²)²+(m²+n²)² is √(2(m⁴ + n⁴)).
Step-by-step explanation:
To simplify the expression √(m² - n²)² + (m² + n²)², let's break it down step-by-step.
1. The expression inside the square root, (m² - n²)², can be simplified by expanding the square. This gives us (m⁴ - 2m²n² + n⁴).
2. Similarly, the expression (m² + n²)² can be simplified by expanding the square. This gives us (m⁴ + 2m²n² + n⁴).
3. Now, let's substitute these simplified expressions back into the original expression:
√[(m⁴ - 2m²n² + n⁴) + (m⁴ + 2m²n² + n⁴)].
4. When we combine like terms within the square root, we get:
√(2m⁴ + 2n⁴).
5. Finally, we can simplify further by factoring out a 2 from the expression under the square root:
√(2(m⁴ + n⁴)).
So, the simplified expression for h is √(2(m⁴ + n⁴)).
Your question is incomplete, but most probably the full question was:
Simplify the expression:
h=√(m²-n²)²+(m²+n²)²