CPM Homework Help : CCA2 Problem 3-46

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.

$(ab)^2$ and $a^2b^2$
Hint (a):
Simplify the first expression.
$(ab)^2=(ab)(ab)=a·a·b·b=a^2b^2$
More Help (a):
Substitute some numbers for $a$ and $b$ to confirm the algebraic manipulations you used are correct.
Answer (a):
The first expression is equivalent to the second expression.

$3x−4y=12$ and $y=\frac{3}{4}x−3$
Hint (b):
Rewrite the first equation in $y=$ form.
More Help (b):
Substitute some numbers for $a$ and $b$ to confirm the algebraic manipulations you used are correct.
Answer (b):
The first equation is equivalent to the second equation.

$y=2(x−1)+3$ and $y=2x+1$
Hint (c):
See part (b).
More Help (c):
Substitute some numbers for $x$ and $y$ to confirm the algebraic manipulations you used are correct.
Answer (c):
The first equation is equivalent to the second equation.

$(a+b)^2$ and $a^2+b^2$
Hint (d):
Remember, $(a+b)^2$ means to square the quantity $a+b$ . You can use a generic rectangle to help you.
More Help (d):
Substitute some numbers for $a$ and $b$ to confirm the algebraic manipulations you used are correct. Remember to be careful about using only $0$ and $1$ . They can work and not work in very specific cases, often worth mentioning.
Answer (d):
The first expression is NOT equivalent to the second expression.

$\frac { x ^ { 6 } } { x ^ { 2 } }$ and $x^3$
Hint (e):
Are these expressions equal for every value of $x$ ?
More Help (e):
This is an example of a place to investigate how using $0$ gives a different result than other numbers.
Answer (e):
The expressions are NOT equivalent except when $x=0$ .

$y=3(x−5)+2$ and $y=2x−8$
Hint (f):
Simplify the first equation.