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Evaluate algebraic expressions by substitution

An algebraic expression represents a numerical quantity determined by the values assigned to its variables; substitution replaces each variable with its assigned integer or rational value while preserving the expression’s structure. Evaluation then applies grouping symbols, exponents, multiplication or division, and addition or subtraction in the correct order, including careful use of parentheses for negative substitutions. Non-integer exponents, symbolic parameters, and formal function evaluation are outside this scope.

Detailed Explanation: Evaluate algebraic expressions by substitution

To evaluate an algebraic expression by substitution:

  1. Replace each variable with its assigned value.
  2. Put negative numbers in parentheses.
  3. Evaluate using the correct order of operations:
    • grouping symbols,
    • exponents,
    • multiplication or division,
    • addition or subtraction.

Example: Evaluate

2a2−3b+52a^2-3b+5

when a=−2a=-2 and b=−1b=-1.

Step 1: Substitute the values.

Replace aa with −2-2 and bb with −1-1:

2(−2)2−3(−1)+52(-2)^2-3(-1)+5

The parentheses around the negative numbers help show exactly what is being substituted.

Step 2: Evaluate the exponent.

(−2)2=4(-2)^2=4

So the expression becomes

2(4)−3(−1)+52(4)-3(-1)+5

Step 3: Multiply.

8+3+58+3+5

Notice that −3(−1)=+3-3(-1)=+3.

Step 4: Add.

8+3+5=168+3+5=16

Therefore,

16\boxed{16}

Learn by doing: Evaluate algebraic expressions by substitution

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    Algebraic Function Variable Substitution - Fractional Terms (Negatives)

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