Calculate \( S_{10} = 3(10)^2 + 5(10) = 300 + 50 = 350 \).
["# Calculate ( S_{10} = 3(10)^2 + 5(10) = 350 ): A Step-by-Step Breakdown", "Understanding how to calculate expressions like ( S_{10} = 3(10)^2 + 5(10) ) is essential for mastering algebra and foundational mathematics. This article walks you through the step-by-step process of evaluating this expression, explaining key concepts along the way and offering practical insights for students and learners.", "## What is ( S_{10} = 3(10)^2 + 5(10) )?", "In algebra, expressions like ( S_{10} ) represent mathematical formulas involving numbers and variables. Here, ( S_{10} ) depends on the value ( 10 ), but it also includes coefficients — specifically coefficients 3 and 5 — and exponential and multiplicative operations. This problem combines powers, multiplication, and addition to form a linear combination evaluated at base 10.", "## Step-by-Step Solution", "Let’s break down the expression:", "[\nS_{10} = 3(10)^2 + 5(10)\n]", "### Step 1: Apply the Exponent First", "According to the order of operations (PEMDAS/BODMAS), exponents are computed before multiplication and addition:", "[\n(10)^2 = 10 \ imes 10 = 100\n]", "Now substitute back:", "[\nS_{10} = 3 \ imes 100 + 5 \ imes 10\n]", "### Step 2: Perform Multiplication", "Now calculate the multiplications:", "[\n3 \ imes 100 = 300\n]\n[\n5 \ imes 10 = 50\n]", "### Step 3: Add the Results Together", "Add the two partial results:", "[\nS_{10} = 300 + 50 = 350\n]", "## Final Result", "[\n\boxed{S_{10} = 350}\n]", "## Why Understanding This Matters", "Evaluating expressions like ( S_{10} ) using exponentiation and arithmetic order helps in solving real-world problems across science, engineering, finance, and computer science. It strengthens foundational math skills and prepares learners for advanced algebra, calculus, and quantitative analysis.", "## Practice Problems", "To strengthen your skills, try calculating similar expressions:", "1. ( S_8 = 2(8)^2 + 4(8) = ? )\n2. ( S_5 = 6(5)^2 + 7(5) = ? )\n3. Simplify ( S_1 = 10(1)^2 + 9(1) )", "Answer:\n1. ( S_8 = 2(64) + 32 = 128 + 32 = 160 )\n2. ( S_5 = 6(25) + 35 = 150 + 35 = 185 )\n3. ( S_1 = 10(1) + 9 = 10 + 9 = 19 )", "## Summary", "Computing ( S_{10} = 3(10)^2 + 5(10) ) follows the order of operations precisely, using powers, multiplication, and addition in sequence. The final answer, 350, illustrates how algebraic expressions build on basic arithmetic operations to produce clear, manageable results.", "By mastering such calculations, you unlock clearer reasoning and stronger problem-solving skills — key tools for academic success and everyday math.", "---", "Keywords for SEO:\nCalculate ( S_{10} = 3(10)^2 + 5(10) ), algebra expression solution, evaluate expressions math, step-by-step math, order of operations, exponents in algebra, scalar multiplication and exponents, solve ( S_{10} = 300 + 50 )", "Meta Description:\nLearn how to calculate ( S_{10} = 3(10)^2 + 5(10) ) step-by-step. Master order of operations with exponents, multiplication, and addition—simple yet powerful in math."]
