CPM Homework Help : CCA2 Problem 3-23

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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.

$(x+3)^2$ and $x^2+9$
Hint (a):
Try substituting numbers for $x$ and simplifying each expression. $0$ and $1$ can give different results, so check them as well as other numbers.
Answer (a):
These two expressions are not equivalent. (But if you had only used $0$ you might have thought they were).

$(x+4)^2$ and $x^2+8x+16$
Hint (b):
Remember that $(x+4)^2$ means $(x+4)(x+4)$ and multiply.
Answer (b):
These two expressions are equivalent.

$(x+1)(2x−3)$ and $2x^2−x−3$
Hint (c):
Multiply and simplify.
Answer (c):
These two expressions are equivalent.

$3(x−4)^2+2$ and $3x^2−24x+50$
Hint (d):
Simplify the first expression and compare. Be sure you read the hint in part (b).

$(x^3)^4$ and $x^7$
Hint (e):
See part (a).

$ab^2$ and $a^2b^2$
Hint (f):
Try substituting numbers for $a$ and $b$ .

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