2%E2%8B%85(mn49n)2.jpeg "(3m−5n24m−2n0)2⋅(mn49n)2")
Simplifying the Expression: (3m−5n24m−2n0)2⋅(mn49n)2
Let's break down the simplification of this expression step by step:
1. Understanding the Expression
The expression involves several multiplications and exponents. It's crucial to remember the order of operations (PEMDAS/BODMAS) to correctly simplify it.
2. Simplifying the Terms within Parentheses
- (3m−5n24m−2n0)2:
- 3m - 5n: This term remains as is, as we can't combine the variables.
- 24m - 2n0: Since any number multiplied by 0 equals 0, this simplifies to 24m.
- (3m - 5n 24m)2: This represents squaring the entire term. We will expand this in the next step.
- (mn49n)2:
- mn: This term remains as is.
- 49n: This simplifies to 49n, as there is no other term to combine it with.
- (mn 49n)2: We will expand this in the next step.
3. Expanding the Squares
- (3m - 5n 24m)2: This expands as (3m - 5n)(3m - 5n)(24m).
- (mn 49n)2: This expands as (mn)(mn)(49n)(49n).
4. Simplifying the Multiplications
- (3m - 5n)(3m - 5n)(24m):
- Multiply the first two terms: (9m² - 15mn - 15mn + 25n²) = (9m² - 30mn + 25n²)
- Multiply the result by 24m: (9m² - 30mn + 25n²) * 24m = 216m³ - 720m²n + 600mn²
- (mn)(mn)(49n)(49n):
- Multiply all the terms: m²n² * 49²n² = 2401m²n⁴
5. Combining the Simplified Terms
Finally, we multiply the simplified terms:
(216m³ - 720m²n + 600mn²) * (2401m²n⁴) = 518616m⁵n⁴ - 1728720m⁴n⁵ + 1440600m³n⁶
Therefore, the simplified form of the expression (3m−5n24m−2n0)2⋅(mn49n)2 is 518616m⁵n⁴ - 1728720m⁴n⁵ + 1440600m³n⁶.