If I were to multiclass Sorcerer 9 Bard 1, could I use an instrument (per Bard Level 1 feature) as my focus for spells that appear on both class spell lists?

For example:

Polymorph, Confusion, Hypnotic Pattern

Thank you

If I were to multiclass Sorcerer 9 Bard 1, could I use an instrument (per Bard Level 1 feature) as my focus for spells that appear on both class spell lists?

For example, Polymorph, Confusion, and Hypnotic Pattern all appear on both lists. Can I use an instrument focus for these if I know them as Sorcerer spells?