a_5 &= 2(5)^2 + 3(5) + 1 = 50 + 15 + 1 = 66. - RTA
Understanding the Equation: 5⁵ = 2(5)² + 3(5) + 1 = 66 – A Step-by-Step Breakdown
Understanding the Equation: 5⁵ = 2(5)² + 3(5) + 1 = 66 – A Step-by-Step Breakdown
Math doesn’t have to be intimidating — even complex expressions can be broken down into simple, understandable steps. In this article, we explore the mathematical expression 2(5)² + 3(5) + 1, show why it adds up to 66, and why mastering such calculations is key to strong numeracy skills.
Understanding the Context
The Equation Explained: From Algebra to Addition
At first glance, the expression 2(5)² + 3(5) + 1 = 66 might look intimidating — but when broken down step by step, it becomes easy to follow. Let’s walk through the full calculation:
Original Expression:
2(5)² + 3(5) + 1
Step 1: Evaluate the Exponent First (Order of Operations)
Using the standard order of operations (PEMDAS/BODMAS), exponents are calculated first:
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Key Insights
- (5)² = 25
Now substitute:
2(25) + 3(5) + 1
Step 2: Perform Multiplication
Now multiply:
- 2 × 25 = 50
- 3 × 5 = 15
Now the expression becomes:
50 + 15 + 1
Step 3: Add the Numbers
Add the terms from left to right:
50 + 15 = 65, then 65 + 1 = 66
So,
2(5)² + 3(5) + 1 = 66
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Why This Matters: Real-World Applications of Polynomials
While this specific equation is algebraic, the principles behind solving it apply widely in math, science, and engineering. Quadratic expressions like 2x² + 3x + 1 are foundational in modeling real-world phenomena — from projectile motion to economic trends. Understanding how to simplify and evaluate such expressions is vital for students, educators, and professionals alike.
Whether you're solving for x in a quadratic equation or verifying algebraic identities, recognizing step-by-step evaluation builds confidence and accuracy.
Tips for Mastering Similar Calculations
-
Follow the Order of Operations (PEMDAS/BODMAS)
Always evaluate exponents first, then multiplication/division, followed by addition and subtraction. -
Simplify Step by Step
Avoid rushing — compute each term individually before combining results. -
Use Parentheses Wisely
Nested parentheses can change the order of evaluation — always prioritize inner expressions first. -
Double-Check Multiplication and Factoring
Check that coefficients are correctly multiplied and like terms are combined properly.
