Question

Which expressions are differences of squares? Select each correct answer

x^2+25
a^2-36
w^2-121
n^2-50

Answer 1

for this ones the second value is always negative so A is not correct. Also they have to have an exact square root which 50 doesn't. So the answers are B and C
(a-6)(a+6)
(w-11)(w+11)

Answer 2

Option B, C and D are correct.

`a^2-36`,
`w^2-121` and
`n^2-50`

Explanation:

For any real number a and b:

Difference of square is given by:

`a^2-b^2 = (a-b)(a+b)`

We have to find Which expressions are differences of squares.

Option A :

`x^2+25`

⇒
`x^2+5^2`

This cannot be written as a difference of square.

Option B:

`a^2-36`

⇒
`a^2-6^2`

⇒
`(a-6)(a+6)`

Option C:

`w^2-121`

⇒
`w^2-11^2`

⇒
`(w-11)(w+11)`

Option D:

`n^2-50`

⇒
`n^2-(√(50))^2`

⇒
`(n-√(50))(n+√(50))`

Therefore, the expressions which are are differences of squares are:

`a^2-36`,
`w^2-121` and
`n^2-50`