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

The simplified form is

`100n^2-1=(10n)^2-1^2`

Explanation:

Given the expression

`100n^2-1`

we have to simplify the above expression.

Expression:
`100n^2-1`

`10^2n^2-1^2`

As
`a^2b^2=(ab)^2`

∴
`10^2n^2-1^2`

⇒
`(10n)^2-1^2`

which is required simplified form.

Option 1 is correct

Answer 2

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

Regroup:
100n^2-1

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

So the correct answer is :
(10n)^2-1^2

To attempt to factor a polynomial of four or more terms with no common factor, first rewrite it in groups. Each group may possibly be separately factored, and the resulting expression may possibly lend itself to further factorization if a greatest common factor or special form is created.