Question

If p = 3, q = 5, find the values of the following algebraic expressions.

(1) p² + q²
(2) p² – 2pq + q²
(3) qp + 3q
(4) p² + 2p + q

Answer 1

(1) p² + q²
Substituting the values of p and q in the given algebraic expression, we get:
(3)² + (5)²
= 9 + 25 (Solving the simple brackets first)
= 34

(2) p² − 2pq + q²
Substituting the values of p and q in the given algebraic expression, we get:
(3)² − 2 × 3 × 5 + (5)²
= 9 − 2 × 3 × 5 + 25 (Solving the simple brackets first)
= 9 − 30 + 25 (Performing multiplication first)
= 34 − 30 (Performing addition first)
= 4

(3) qp + 3q
Substituting the values of p and q in the given algebraic expression, we get:
5 × 3 + 3 × 5
= 15 + 15 (Performing multiplication first)
= 30

(4) p² + 2p + q
Substituting the values of p and q in the given algebraic expression, we get:
(3)² + 2 × 3 + 5
= 9 + 2 × 3 + 5 (Solving the simple brackets first)
= 9 + 6 + 5 (Performing multiplication first)
= 20