Question

Prove: 5 · n · (4 · n) = 20n^2

Statements Reasons

5 · n · (4 · n) = 5 · n · (n · 4) Commutative Property of Multiplication
5 · n^2 · 4 Multiplication
5 · 4 · n^2 Commutative Property of Multiplication
20 · n^2 Multiplication

Answer 1

The statement 5 · n · (4 · n) = 20n^2 is true.

Step-by-step explanation:

Statements:

5 · n · (4 · n)

5 · n · (n · 4) (Commutative Property of Multiplication)

5 · n^2 · 4 (Multiplication)

5 · 4 · n^2 (Commutative Property of Multiplication)

20 · n^2 (Multiplication)

Reasons:

Given statement.

The Commutative Property states that the order of multiplication does not affect the product.

Here, we rearrange the factors without changing the value.

We multiply 5 and 4.

Again, we apply the Commutative Property.

We multiply 20 and n^2 to get the final result.

Therefore, we have shown that 5 · n · (4 · n) = 20n^2 through a series of valid steps based on the Commutative Property of Multiplication and basic multiplication rules.