If a = 3, b = 4 and c = −2, find the values of the following algebraic expressions.

(1) 2a + 5b
(2) a + b + c
(3) b² + a² − c²
(4) b² − a²

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Solution

(1) 2a + 5b
Substituting the values of a and b in the given algebraic expression, we get:
2 × 3 + 5 × 4
= 6 + 20 (Performing multiplication first)
= 26

(2) a + b + c
Substituting the values of a, b and c in the given algebraic expression, we get:
3 + 4 − 2
= 7 − 2 (Performing addition first)
= 5

(3) b² + a² − c²
Substituting the values of a, b and c in the given algebraic expression, we get:
(4)² + (3)² − (−2)²
= 16 + 9 − 4 (Solving the simple brackets first)
= 25 − 4 (Performing addition first)
= 21

(4) b² − a²
Substituting the values of a and b in the given algebraic expression, we get:
(4)² − (3)²
= 16 − 9 (Solving the simple brackets first)
= 7

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