Evaluating Algebraic Expressions
Evaluating algebraic expressions means substituting given values for variables and computing the result in Grade 8 math (Yoshiwara Core Math). Substitute each variable with its value, then apply the correct order of operations. For x = 3, y = 2: 4x² − y = 4(9) − 2 = 34. Common errors: forgetting to apply exponents before multiplying, and mishandling negative substitutions (use parentheses: (−5)² = 25, not −25). This skill is prerequisite for understanding functions and verifying equation solutions.
Key Concepts
Property When we evaluate an algebraic expression, we follow the order of operations. Order of Operations: 1. Perform any operations inside parentheses, or above or below a fraction bar. 2. Compute all powers and roots. 3. Perform all multiplications and divisions from left to right. 4. Perform additions and subtractions from left to right.
Examples Evaluate $30 4x^2$ for $x=2$. Substitute: $30 4(2)^2$. Power first: $30 4(4)$. Then multiply: $30 16$. Finally, subtract: $14$. Evaluate $(10 c)^2$ for $c=3$. Substitute: $(10 3)^2$. Parentheses first: $(7)^2$. Then compute the power: $49$. Evaluate $2(a^2 + 1)$ for $a=5$. Substitute: $2(5^2+1)$. Inside parentheses, do the power first: $2(25+1)$. Then add: $2(26)$. Finally, multiply: $52$.
Explanation Evaluating an expression means finding its final numerical value. The Order of Operations (PEMDAS) is the universal rulebook that ensures everyone gets the same answer from the same calculation. Always follow the steps precisely.
Common Questions
How do you evaluate an algebraic expression?
Replace each variable with its given value, then calculate using the correct order of operations.
What order of operations applies?
Parentheses → Exponents → Multiplication/Division → Addition/Subtraction (PEMDAS).
How do you evaluate 4x² − y when x = 3, y = 2?
4(3²) − 2 = 4(9) − 2 = 36 − 2 = 34.
How do you handle negative value substitutions?
Use parentheses. x² when x = −5: (−5)² = 25, not −25.
What is the difference between an expression and an equation?
An expression (3x + 2) has no equals sign and is evaluated. An equation (3x + 2 = 11) has an equals sign and is solved.