Factor 4x^2-25
Factor polynomials completely: trinomials, difference of squares, sum/difference of cubes.
To factor 4x^2-25, recognize this as a difference of two squares — a² − b² = (a + b)(a − b).
4x2-25
This expression has two terms connected by subtraction, and both are perfect squares. This matches the difference of squares pattern.
The identity states:
a2 − b2 = (a + b)(a − b)
Identify a and b:
a = 2x (since (2x)2 gives the first term)
b = 5 (since 52 = 25)
Substitute a and b into (a + b)(a − b):
= (2x + 5)(2x − 5)
(2x - 5)(2x + 5)
How to factor 4x^2-25
To factor 4x^2-25, identify the type of polynomial and apply the appropriate technique. The factored form is (2x - 5)(2x + 5).
This is a polynomial factoring problem — we break a polynomial into a product of simpler expressions. Common methods include GCF extraction, difference of squares, and trinomial factoring.
Frequently asked questions
What is the answer to 4x^2-25?
The answer is (2x - 5)(2x + 5).
What method is used?
identifying the polynomial type and applying the matching technique — GCF, trinomial factoring, difference of squares, or special cube formulas.