### Home > CAAC > Chapter 13 > Lesson 13.RE2-S > Problem 2-135

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 ✎(

*x*+ 3)^{2}and*x*^{2}+ 9(

*x*+ 4)^{2}and*x*^{2}+ 8*x*+ 16(

*x*+ 1)(2*x*− 3) and 2*x*^{2}−*x*− 33(

*x*− 4)^{2}+ 2 and 3*x*^{2}− 24*x*+ 50(

*x*^{3})^{4}and*x*^{7}*ab*^{2}and*a*^{2}*b*^{2}

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*.