Question

Which expressions correctly demonstrate the Commutative Property?
3x(9y+6)=(3x+9y)⋅6
3 x left parenthesis 9 y plus 6 right parenthesis equals left parenthesis 3 x plus 9 y right parenthesis times 6

3x⋅9y⋅6=9y+6+3x
3 x times 9 y times 6 equals 9 y plus 6 plus 3 x

3x⋅9y⋅6=9y⋅6⋅3x
3 x times 9 y times 6 equals 9 y times 6 times 3 x

3x⋅9y⋅6=162xy
3 x times 9 y times 6 equals 162 x y

Answer 1

According to the Associative Property of Addition, which of the following is equivalent to the expression (b+c)+a+d?
d+a+(b+c)
d plus a plus left parenthesis b plus c right parenthesis

d+(b+c)+a
d plus left parenthesis b plus c right parenthesis plus a

b+(c+a)+d
b plus left parenthesis c plus a right parenthesis plus d

(b+c)+d+a
left parenthesis b plus c right parenthesis plus d plus a

Answer 2

Are you sure?

Answer 3

What is the difference between the expression (3x+4x)+2x and the expression 3x+(4x+2x)?
3x
2x
0
4x

Answer 4

Which of the following equations demonstrates the Associative Property?]
3x⋅(4x+5x)=(3x+4x)⋅5
3 x times open paren 4 x plus 5 x close paren is equal to open paren 3 x plus 4 x close paren times 5 - no response given

(3x+4x)⋅5=3x+(4x⋅5)
open paren 3 x plus 4 x close paren times 5 is equal to 3 x plus open paren 4 x times 5 close paren - incorrect

3x⋅(4x⋅5)=(3x⋅4x)⋅5
3 x times open paren 4 x times 5 close paren is equal to open paren 3 x times 4 x close paren times 5 - no response given

3x⋅(4x⋅5)=3x(4x+5)
3 x times open paren 4 x times 5 close paren is equal to 3 x open paren 4 x plus 5 close paren - no response given

Answer 5

Which expression is equivalent to (3r⋅5)⋅(−3⋅8)?
15r⋅(5⋅8)
15 r times left parenthesis 5 times 8 right parenthesis

24r⋅(5⋅−3)
24 r times left parenthesis 5 times negative 3 right parenthesis

−45r⋅5
negative 45 r times 5

(5⋅−3)⋅−9r
left parenthesis 5 times negative 3 right parenthesis times negative 9 r

Answer 6

Use the Distributive Property to rewrite the expression (3x−5)(2x+2)?
x2−3x−10
x squared minus 3 x minus 10

6x2−4x−10
6 x squared minus 4 x minus 10

5x2−2x−3
5 x squared minus 2 x minus 3

6x2−3x−10
6 x squared minus 3 x minus 10

Answer 7

Use the Distributive Property to write the expression 4x^2−36 a different way.
(x+18)(x−18)
left parenthesis x plus 18 right parenthesis left parenthesis x minus 18 right parenthesis

(2x+9)(x−9)
left parenthesis 2 x plus 9 right parenthesis left parenthesis x minus 9 right parenthesis

(2x+6)(2x−6)
left parenthesis 2 x plus 6 right parenthesis left parenthesis 2 x minus 6 right parenthesis

4x(x−9)
4 x left parenthesis x minus 9 right parenthesis

Answer 8

That is wrong bot

Answer 9

The correct expressions that demonstrate the Commutative Property are:

3x(9y+6)=(3x+9y)⋅6

3x⋅9y⋅6=9y⋅6⋅3x

Answer 10

According to the Associative Property of Addition, the expression (b+c)+a+d is equivalent to (b+c)+d+a.

Answer 11

Apologies for the mistake. You are correct, according to the Associative Property of Addition, the expression (b+c)+a+d is equivalent to b+(c+a)+d.

Answer 12

The difference between the expressions (3x+4x)+2x and 3x+(4x+2x) lies in the grouping of the terms.

In the expression (3x+4x)+2x, we first add the like terms 3x and 4x to get 7x, and then add 2x to get the final result of 9x.

On the other hand, in the expression 3x+(4x+2x), we first group the terms (4x+2x) and add them to get 6x, and then add 3x to get the final result of 9x.

Therefore, both expressions simplify to 9x, and the difference between them is 0.

Answer 13

The equation that demonstrates the Associative Property is:

3x⋅(4x⋅5)=(3x⋅4x)⋅5

This equation shows that the multiplication can be regrouped by associating (4x⋅5) together and then multiplying it by 3x, or by associating (3x⋅4x) together and then multiplying it by 5.

Answer 14

The expression that is equivalent to (3r⋅5)⋅(−3⋅8) is:
24r⋅(5⋅−3) or 24 r times left parenthesis 5 times negative 3 right parenthesis

Answer 15

The expression (3x−5)(2x+2) rewritten using the Distributive Property is:

6x² - 4x - 10

So the correct answer is 6x² - 4x - 10.

Answer 16

The expression 4x^2−36 can be rewritten using the Distributive Property as:

4x(x−9)

So the correct answer is 4x(x−9).

Answer 17

Apologies for the incorrect response earlier. You are right, the correct way to write the expression 4x^2−36 using the distributive property is (2x+6)(2x-6). Thank you for pointing out the mistake.