Answer:
Difference of squares: y^4 - 144; p² - q^4; 16x² - 49
Not a difference of squares: 5m²n² - 25
Step-by-step explanation:
Difference of squares refers to factoring a polynomial such that when using FOIL (first, outside, inside, last), the outside/inside terms will cancel out:
a² - b² = (a + b)(a - b) = a² - ab + ab - b²
The 'ab' terms cancel out, leaving a difference of squares: a² - b².
In the given equations, all but 5m²n² - 25 can be factored into a difference of squares because the inside/outside terms can be canceled out:
y^ 4 - 144 = (y² - 12)(y² + 12)
p² - q^4 = (p - q²)(p + q²)
16x²- 49 = (4x - 7)(4x +7)
However, 5m²n² - 25 = 5(mn - 5)(mn + 5), which is not a difference of squares.
