Simplifying Algebraic Expressions
Learn to combine like terms and simplify expressions with variables.
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What is an Algebraic Expression?
An algebraic expression is a mathematical phrase that contains numbers, variables (letters), and operations. For example:
$$3x + 2y - 5$$
Here, x and y are variables, 3 and 2 are coefficients, and -5 is a constant.
Combining Like Terms
Like terms are terms that have the same variable raised to the same power. We can add or subtract them.
Example 1: Simplify $4x + 3x$
$$4x + 3x = (4+3)x = 7x$$
Example 2: Simplify $5a + 3b - 2a + b$
$$5a + 3b - 2a + b = (5a - 2a) + (3b + b) = 3a + 4b$$
Watch out! You can only combine terms with the same variable. You cannot combine $3x + 2y$ into $5xy$. These are different terms!
Using Python to Check Your Work
You can use Python to verify algebraic simplifications:
from sympy import symbols, simplify
x, y = symbols('x y')
# Define the expression
expr = 5*x + 3*y - 2*x + y
# Simplify
simplified = simplify(expr)
print(f"Original: 5x + 3y - 2x + y")
print(f"Simplified: {simplified}")
# Output: Simplified: 3*x + 4*yPractice Problems
- Simplify: $7m - 3m + 2n$
- Simplify: $2a + 4b - a + 3b - 5$
- Expand and simplify: $3(x + 2) - 2(x - 1)$
Show Solutions
1. $7m - 3m + 2n = 4m + 2n$
2. $2a + 4b - a + 3b - 5 = a + 7b - 5$
3. $3(x + 2) - 2(x - 1) = 3x + 6 - 2x + 2 = x + 8$
Pro Tip: Always write like terms in alphabetical order ($a$ before $b$, $x$ before $y$) to keep your work organized.
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Algebraic Expressions
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