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3-23.

Decide whether each of the following pairs of expressions are equivalent for all values of x (or a and b). If they are equivalent, show how you can be sure. If they are not, justify your reasoning completely. Homework Help ✎

  1. and

    Try substituting numbers for x and simplifying each expression. 0 and 1 can give different results, so check them as well as other numbers.

    These two expressions are not equivalent. (But if you had only used 0 you might have thought they were).

  2. and

    Remember that means and multiply.

    These two expressions are equivalent.

  3. and

    Multiply and simplify.

    These two expressions are equivalent.

  4. and

    Simplify the first expression and compare. Be sure you read the hint in part (b).

  5. and

    See part (a).

  6. and

    Try substituting numbers for and .