Question

Select all the expressions that are equivalent to 78 • 7.
73 • 73
71879

(73)3
74 + 75
74 • 75

Answer 1

To find the expressions that are equivalent to \( 78 \cdot 7 \), we can evaluate the provided options:

1. **\( 73 \cdot 73 \)**:
\[
73 \cdot 73 = 5329
\]
(This is not equivalent.)

2. **\( 71879 \)**:
(This is just a number and does not equal \( 78 \cdot 7 \).)

3. **\( (73)^3 \)**:
\[
73^3 = 73 \cdot 73 \cdot 73 = 389017
\]
(This is not equivalent.)

4. **\( 74 + 75 \)**:
\[
74 + 75 = 149
\]
(This is not equivalent.)

5. **\( 74 \cdot 75 \)**:
Using the identity \( (a + b)(a - b) = a^2 - b^2 \) where \( a = 75 \) and \( b = 1 \):
\[
74 \cdot 75 = (75 - 1) \cdot 75 = 75^2 - 75 = 5625 - 75 = 5550
\]
(This is also not equivalent.)

Now, let's directly calculate \( 78 \cdot 7 \):
\[
78 \cdot 7 = 546
\]

None of the provided options are equivalent to \( 78 \cdot 7 = 546 \).

Therefore, **the answer is: none of the expressions are equivalent to \( 78 \cdot 7 \)**.