Math Problem Statement
25(m squared plus 1) Squared - 9 (n sqaured minus 5) squared
Solution
The expression you've provided is:
Let's simplify it step-by-step.
Step 1: Expand both squared terms
First, expand each of the squared binomials.
For the first part: Now, multiply by 25:
For the second part: Now, multiply by 9:
Step 2: Combine both parts
Now substitute these into the original expression:
Simplify by distributing the negative sign:
Now, combine like terms:
Final Simplified Expression:
Would you like further clarification or have any specific questions on the steps? Here are some related questions to deepen your understanding:
- How do you factor expressions like this if needed?
- What would happen if we substituted specific values for and ?
- How would the result change if the numbers 25 and 9 were swapped in the original expression?
- Can this expression be factored further, and if so, how?
- How do we handle higher powers of and in algebraic simplifications?
Tip: Always expand binomials before trying to combine or simplify terms. This helps avoid mistakes and makes the problem easier to manage.
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Math Problem Analysis
Mathematical Concepts
Algebra
Binomial Expansion
Polynomials
Formulas
(a + b)^2 = a^2 + 2ab + b^2
(a - b)^2 = a^2 - 2ab + b^2
Theorems
Difference of squares
Suitable Grade Level
Grades 9-11