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Remembering

Use Simplify and Expand:

expr := (x + 2)^2 - (x - 3)^2 Simplify[expr] Expand[expr]

Factor and verify:

Factor[x^2 + 5x + 6] Expand[(x + 2)(x + 3)]

Substitute into expressions:

Substitute[f(x), x = x + 1] Substitute[f(x), x = g(x)]