### Home > CCA2 > Chapter 3 > Lesson 3.1.2 > Problem3-23

3-23.

Decide whether each of the following pairs of expressions are 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. $(x+3)^2$ 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. $(x+4)^2$ and $x^2+8x+16$

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

These two expressions are equivalent.

1. $(x+1)(2x−3)$ and $2x^2−x−3$

Multiply and simplify.

These two expressions are equivalent.

1. $3(x−4)^2+2$ and $3x^2−24x+50$

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

1. $(x^3)^4$ and $x^7$

See part (a).

1. $ab^2$ and $a^2b^2$

Try substituting numbers for $a$ and $b$.