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

Answer:

Option B, C and D are correct.

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

Step-by-step 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:

$n^2-50$

⇒$n^2-(\sqrt{50})^2$

⇒$(n-\sqrt{50})(n+\sqrt{50})$

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

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