Convert and expand to canonical SOP form Given the Boolean expression LM + M(NO + PQ), convert it explicitly into a sum-of-products (SOP) expression by distributing terms and listing the distinct product terms.

Introduction / Context:
Sum-of-products (SOP) form is widely used in digital design because it maps naturally to two-level AND–OR implementations and to programmable logic arrays. Converting any given Boolean expression into SOP ensures that each term is a product (AND) of literals, summed (ORed) together.

Given Data / Assumptions:

• Expression: LM + M(NO + PQ).
• Operators: adjacency = AND, “+” = OR.
• No complements are shown; all literals are in positive form unless implied.

Concept / Approach:
To obtain SOP, first expand any parentheses using the distributive property: X(Y + Z) = XY + XZ. Then collect the resulting product terms. Each product term is an AND of literals; the final expression is an OR of these products.

Step-by-Step Solution:

Verification / Alternative check:
Each term is a product of literals (LM, MNO, MPQ). There are no sums inside products, so it satisfies SOP. A quick truth-table spot check on a few input combinations confirms functional equivalence before and after expansion.

Why Other Options Are Wrong:

• LM + MNOPQ: Introduces an incorrect five-literal term by multiplying N, O, P, and Q together.
• L + MNO + MPQ: Drops M from LM and incorrectly replaces it with L alone.
• LM + M + NO + MPQ: NO is not gated by M, and “M” as a standalone term alters the function.

Common Pitfalls:
Forgetting to distribute to all terms; accidentally multiplying all symbols together; or incorrectly simplifying by removing necessary literals. Always keep track of each literal during distribution.

Final Answer:
LM + MNO + MPQ