Hello there!
Our question is:
"Which expression is equivalent to 56 + 21?
A.) 7(49 + 14)
B.) 8(7 + 21)
C.) 8(48 + 13)
D.) 7(8 + 3)"
It appears our question wants us to answer our question with two-step expressions by applying the Distributive Property.
The Distributive Property allows any number/variable outside a parenthesis (with no order of operation symbol between the number/variable and the parenthesis) to multiply by all numbers/variables inside the parenthesis.
For example, this is how to properly apply the Distributive Property;
2(1 + 3)
2(1) + 2(3)
2 + 6
This is NOT how to properly apply the Distributive Property;
2(1 + 3)
2 + 4
Now that we've covered the basics of what we're dealing with, let's try to solve our question using the Distributive Property on our answer choices.
A.) 7(49 + 14);
7(49) + 7(14)
343 + 98.
343 + 98 [tex] \neq [/tex] 56 + 21
B.) 8(7 + 21);
8(7) + 8(21)
56 + 126.
56 + 126 [tex] \neq [/tex] 56 + 21
C.) 8(48 + 13)
8(48) + 8(13)
384 + 104
384 + 104 [tex] \neq [/tex] 56 + 21
Now, all we are left with is D, likely making it our only correct answer, but let's test it out anyways.
D.) 7(8 + 3);
7(8) + 7(3)
56 + 21
56 + 21 = 56 + 21
Your correct answer is D.) 7(8 + 3).
I hope this helps!
If you have any questions or concerns as to how I came to my answer or how to handle this, feel free to send me a message and I will respond asap. :)
