Simplify Equation Calculator

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Algebraic Expression Simplifier

Simplified Result:

function calculateSimplification() { var coeffX = parseFloat(document.getElementById("coeffX").value); var valX = parseFloat(document.getElementById("valX").value); var coeffY = parseFloat(document.getElementById("coeffY").value); var valY = parseFloat(document.getElementById("valY").value); var constantC = parseFloat(document.getElementById("constantC").value); if (isNaN(coeffX) || isNaN(valX) || isNaN(coeffY) || isNaN(valY) || isNaN(constantC)) { document.getElementById("simplifiedResult").innerText = "Please enter valid numbers for all fields."; return; } // The expression to simplify is Ax + By + C var result = (coeffX * valX) + (coeffY * valY) + constantC; document.getElementById("simplifiedResult").innerText = result.toFixed(2); }

Understanding Algebraic Expression Simplification

Algebraic expressions are fundamental building blocks in mathematics, consisting of variables, coefficients, constants, and mathematical operations. Simplifying an algebraic expression often means reducing it to its most basic form, which can involve combining like terms, distributing, or, as in the case of this calculator, evaluating the expression by substituting specific numerical values for its variables.

What is an Algebraic Expression?

An algebraic expression is a mathematical phrase that can contain numbers, variables (like x, y, z), and operation symbols (like +, -, ×, ÷). Unlike an equation, an expression does not contain an equals sign. For example, 2x + 3y - 10 is an algebraic expression.

How This Calculator Simplifies Expressions

This calculator focuses on simplifying a linear algebraic expression of the form Ax + By + C by substituting given numerical values for the variables 'x' and 'y', and then performing the arithmetic operations. This process reduces the entire expression to a single numerical value, effectively "simplifying" it from a variable-dependent form to a concrete number.

The formula used is straightforward:

Simplified Result = (A × x) + (B × y) + C

  • A: The coefficient (multiplier) of the variable 'x'.
  • x: The numerical value assigned to the variable 'x'.
  • B: The coefficient (multiplier) of the variable 'y'.
  • y: The numerical value assigned to the variable 'y'.
  • C: The constant term, which is a number without any variables.

Practical Examples

Let's look at how this simplification works with real numbers:

Example 1: Basic Evaluation

Consider the expression: 2x + 3y - 10

If we set:

  • Coefficient of x (A) = 2
  • Value of x = 5
  • Coefficient of y (B) = 3
  • Value of y = 2
  • Constant Term (C) = -10

Using the formula:

Simplified Result = (2 × 5) + (3 × 2) + (-10)

Simplified Result = 10 + 6 – 10

Simplified Result = 16 – 10

Simplified Result = 6

Example 2: With Negative Values

Consider the expression: -4x + 0.5y + 7

If we set:

  • Coefficient of x (A) = -4
  • Value of x = 3
  • Coefficient of y (B) = 0.5
  • Value of y = -8
  • Constant Term (C) = 7

Using the formula:

Simplified Result = (-4 × 3) + (0.5 × -8) + 7

Simplified Result = -12 + (-4) + 7

Simplified Result = -12 – 4 + 7

Simplified Result = -16 + 7

Simplified Result = -9

This calculator is a useful tool for quickly evaluating algebraic expressions when you have specific values for the variables, helping you to understand the numerical outcome of a given algebraic relationship.

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