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Simplify

Simplify

To use the rules of arithmetic and algebra to rewrite an expression as simply as possible.

 

Two worked examples: simplifying 2x−3+5+8x to 10x+2, and (x−1)²−(x+1)² to −4x.

Worked Example

Problem: Simplify the expression 3x + 2(4x − 5) + 10.
Step 1: Distribute the 2 across the parentheses.
3x+2(4x−5)+10=3x+8x−10+103x + 2(4x - 5) + 10 = 3x + 8x - 10 + 10
Step 2: Combine like terms: group the x-terms together and the constant terms together.
3x+8x=11xand−10+10=03x + 8x = 11x \qquad \text{and} \qquad -10 + 10 = 0
Step 3: Write the simplified expression.
11x11x
Answer: The simplified expression is 11x11x.

Another Example

Problem: Simplify the fraction 36/48.
Step 1: Find the greatest common factor (GCF) of 36 and 48. The factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18, 36. The factors of 48 include 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The GCF is 12.
GCF(36,48)=12\text{GCF}(36, 48) = 12
Step 2: Divide both the numerator and the denominator by the GCF.
3648=36÷1248÷12=34\frac{36}{48} = \frac{36 \div 12}{48 \div 12} = \frac{3}{4}
Answer: The simplified fraction is 34\frac{3}{4}.

Frequently Asked Questions

What does it mean to simplify in math?
To simplify means to rewrite an expression in a shorter or less complicated form that has the same value as the original. This can involve combining like terms, reducing fractions, applying exponent rules, or performing arithmetic operations. The goal is to make the expression as clean and compact as possible.
Is simplifying the same as solving?
No. Simplifying means rewriting an expression in a reduced form—you are not finding the value of a variable. Solving means finding the value(s) of a variable that make an equation true. For example, you simplify 2x+3x2x + 3x to 5x5x, but you solve 5x=205x = 20 to get x=4x = 4.

Simplify vs. Solve

Simplifying reduces an expression to a simpler equivalent form (e.g., 6x+2x6x + 2x becomes 8x8x). Solving finds the unknown value that satisfies an equation (e.g., 8x=248x = 24 gives x=3x = 3). When you simplify, you do not find a numerical answer for a variable—you just make the expression cleaner. When you solve, your end result is a specific value or set of values.

Why It Matters

Simplifying is one of the most frequently used skills across all areas of math. Reducing expressions before solving equations makes the algebra easier and less error-prone. In real-world applications—from physics formulas to financial calculations—working with the simplest form of an expression saves time and reduces the chance of arithmetic mistakes.

Common Mistakes

Mistake: Combining terms that are not like terms, such as adding 3x3x and 4x24x^2 to get 7x27x^2 or 7x37x^3.
Correction: You can only combine terms with the same variable raised to the same power. 3x3x and 4x24x^2 are not like terms, so 3x+4x23x + 4x^2 is already simplified.
Mistake: Forgetting to distribute a negative sign or coefficient to every term inside parentheses, e.g., writing −(3x−2)=−3x−2-(3x - 2) = -3x - 2.
Correction: The negative sign (or coefficient) must multiply each term inside the parentheses: −(3x−2)=−3x+2-(3x - 2) = -3x + 2. The sign of every term flips.

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