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 x2 + 9
(x + 4)2 and x2 + 8x + 16
(x + 1)(2x − 3) and 2x2 − x − 3
3(x − 4)2 + 2 and 3x2 − 24x + 50
(x3)4 and x7
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.