Question

which expression is equivalent to 100 n2 − 1? (10n)2 − (1)2 (10n2)2 − (1)2 (50n)2 − (1)2 (50n2)2 − (1)2

Answer 1

Answer:

The expression  100n² - 1 is equivalent to (10n)² - 1² .

Step-by-step explanation:

As given the expression in the question be as follow

= 100n² - 1

Take

= (10n)² - 1²

As

(10n)² = 100n²

1² = 1

Put in these values in the expression

=  (10n)² - 1²

= 100n² - 1

Therefore the expression  100n² - 1 is equivalent to (10n)² - 1² .

Answer 2

You know that $100=10^2$.

Use the property $(ab)^2=a^2\cdot b^2$ to state that

$100n^2=10^2\cdot n^2=(10n)^2.$

Then the expression $100n^2-1$ is equivalent to

$(10n)^2-1=(10n)^2-1^2.$

Answer: correct choice is A.