difference of squares means that both the terms are square terms. (also there must be a - symbol)
for example
y^2 - 4
square root of y^2 is y
square root of 4 is +2 as well as -2
so you would factorise it like this:
(y+2)(y-2)
1. y^4 has a square root of y^2 as y^2 × y^2 is y^4.
however, -2 doesnt have a whole number square root so it is not a difference of squares.
2. 25 has a square root of 5. m^2 has a square root of m. n^4 has a square root of n^2. so this 25m^2n^4 is a square term.
1 has a square root of +1 and -1.
therefore, this one is a difference of squares. (5mn^2 +1) (5mn^2 -1)
3. p^8 has a square root of p^4. q^4 has a square root of +q^2 and -q^2)
so it is a difference of squares. (p^4+q^2)(p^4 -q^2)
4. 16x^2 is a square term as irs square root is 4x.
however, 24 is not a square term.
therefore, it is not a difference of squares.
