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Home > A2C > Chapter 2 > Lesson 2.2.2 > Problem 2-135

2-135.
  1. Decide whether each of the following pairs of expressions or equations is 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. (x + 3)2 and x2 + 9

    2. (x + 4)2 and x2 + 8x + 16

    3. (x + 1)(2x − 3) and 2x2x − 3

    4. 3(x − 4)2 + 2 and 3x2 − 24x + 50

    5. (x3)4 and x7

    6. ab2 and a2b2

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).

Multiply and simplify.

These two expressions are equivalent.

See part (a).

Remember that (x + 4)2 means (x + 4)(x + 4) and multiply.

These two expressions are equivalent.

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

Try substituting numbers for a and b.