Home > A2C > Chapter 2 > Lesson 2.2.2 > Problem2-135

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.

1. $\left(x + 3\right)^{2} \text{ and } x^{2} + 9$

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).

1. $\left(x + 4\right)^{2} \text{ and } x^{2} + 8x + 16$

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

These two expressions are equivalent.

1. $\left(x + 1\right)\left(2x − 3\right) \text{ and } 2x^{2} − x − 3$

Multiply and simplify.

These two expressions are equivalent.

1. $3\left(x − 4\right)^{2} + 2 \text{ and } 3x^{2} − 24x + 50$

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

1. $\left(x^{3}\right)^{4} \text{ and } x^{7}$

See part (a).

1. $ab^{2} \text{ and } a^{2}b^{2}$

Try substituting numbers for a and b.