Substitute values for variables in a polynomial to find the value of the expression. The key point is to simplify the expression before substituting.
Basics of Substitution
When substituting a number for a variable, always use parentheses.
Example ①
When x = 3、y = −2, find the value of 3x − 2y.
Answer:3×(3) − 2×(−2) ＝ 9 + 4 ＝ 13。
When x = 3、y = −2, find the value of 3x − 2y.
Answer:3×(3) − 2×(−2) ＝ 9 + 4 ＝ 13。
Substitute After Simplifying
Example ②
When a = −2, find the value of (3a + 5) − (a − 4).
Answer:First simplify: 2a + 9. Substitute a=−2: −4 + 9 ＝ 5。
When a = −2, find the value of (3a + 5) − (a − 4).
Answer:First simplify: 2a + 9. Substitute a=−2: −4 + 9 ＝ 5。
Value of a Product of a Polynomial and a Monomial
Example ③
When x = 4, find the value of 2x(x − 3) − x(x + 1).
Answer:Simplify → x² − 7x. x=4 → 16 − 28 ＝ −12。
When x = 4, find the value of 2x(x − 3) − x(x + 1).
Answer:Simplify → x² − 7x. x=4 → 16 − 28 ＝ −12。
Key Points
- Always use parentheses when substituting
- Simplify long expressions before substituting
- Remember that (−a)² = a²
- “Simplify first” saves time
Practice Problems
- When x = −3、y = 4, find the value of −2x + 5y
- When a = 2, find the value of (4a − 1) + (a + 7)
- When x = −1, find the value of 3x(x − 2) − x(2x + 5)
Answers and Explanations
- Answer:26
Explanation: 6+20=26。 - Answer:16
Explanation:Simplify → 5a+6. a=2→16。 - Answer:12
Explanation:Simplify → x²−11x. x=−1→1+11=12。