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Replacing a sub-expression with scalar multiples means substituting a term or a combination of terms in an equation with a scalar multiple of that term or combination. This is often done to simplify the expression or to manipulate it in some way. For example, if you have an equation containing a term like 2x + 4y, you could replace it with 2(2x + 4y) = 4x + 8y to make it easier to work with. Conversely, if you have an equation with a term like 4x + 8y, you could replace it with 2(2x + 4y) to factor out a common factor of 2.