Factorise 5p³ – p²q + 10p²q – 2pq² + 5pq² – q³

Group and simplify like terms first: 5p³ plus parenthesis negative p²q plus 10p²q plus parenthesis negative 2pq² plus 5pq² minus q³. This becomes 5p³ plus 9p²q plus 3pq² minus q³. Actually, let me regroup the original: 5p³ minus p²q plus 10p²q equals 5p³ plus 9p²q. And negative 2pq² plus 5pq² equals 3pq². So expression is 5p³ plus 9p²q plus 3pq² minus q³.

Try factoring by grouping or pattern recognition. Notice this might factor as parenthesis p plus q ² times something. Expand parenthesis p plus q ² equals p² plus 2pq plus q². We need a third factor. Test the options by expanding.

Expand parenthesis p plus q ² times parenthesis 5p minus q: parenthesis p² plus 2pq plus q² times parenthesis 5p minus q. Multiply: 5p³ minus p²q plus 10p²q minus 2pq² plus 5pq² minus q³. This matches the original expression exactly.