What is the value of a(a + b² + c) + b²(a² + b² + c²) - c(a + b²), when a = 1,…

Concept: To evaluate an algebraic expression at given values of its variables, substitute every variable first and compute any powers — squaring a negative number gives a positive result — then combine the terms exactly in the order and operation the expression specifies.

1. Substitute a = 1, b = -3 and c = -2, and work out the squares needed: b2 = 9, a2 = 1 and c2 = 4.

2. First term: a(a + b2 + c) = 1 × (1 + 9 - 2) = 1 × 8 = 8.

3. Second term: b2(a2 + b2 + c2) = 9 × (1 + 9 + 4) = 9 × 14 = 126.

4. Third term: -c(a + b2) = -(-2) × (1 + 9) = 2 × 10 = 20.

5. Add the three results: 8 + 126 + 20 = 154.

Cross-check: Expanding the expression symbolically first, a(a + b2 + c) + b2(a2 + b2 + c2) - c(a + b2) simplifies to a2 + ab2 + a2b2 + b4 + b2c2 - b2c (the +ac and -ca terms cancel). Substituting the same values gives 1 + 9 + 9 + 81 + 36 + 18 = 154, confirming the value obtained above.