How do you expand 5b plus 5c in algebra?

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It IS expanded.
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How do you solve 10a plus 5b?

You can't just solve one side of the equation. You always have to have both sides of the equal sign in order to manipulate the terms. If you have an equation like 10a + 5b=

Is 5b plus 14 an equation?

No unfortunately this is not an equation. An equation must end with an equals sign. 5b + 14 is simply two terms.