### Home > AC > Chapter 13 > Lesson 13.RE3-S > Problem 2-150

Decide whether each of the following pairs of expressions or equations are equivalent. If they are, show how you can be sure. If they are not, justify your reasoning completely.

and Simplify the first expression.

Substitute some numbers for

*a*and*b*to confirm the algebraic manipulations you used are correct.The first expression is equivalent to the second expression.

and Rewrite the first equation in

*y*-form.Substitute some numbers for

*a*and*b*to confirm the algebraic manipulations you used are correct.The first equation is equivalent to the second expression.

andSee part (b).

Substitute some numbers for

andto confirm the algebraic manipulations you used are correct.The first equation is equivalent to the second equation.

and Remember,

means to square the quantity You can use a generic rectangle to help you.Substitute some numbers for

andto confirm the algebraic manipulations you used are correct. Remember to be careful about using onlyand . They can work and not work in very specific cases, often worth mentioning. The first expression is NOT equivalent to the second expression.

and Are these expressions equal for every value

*x*?This is an example of a place to investigate how using

gives a different result than other numbers. The expressions are equivalent except when

.

andSimplify the first equation.