Factoring 4x² - 25

Algebra 1 · Axiom Academy

Recognize a difference of two perfect squares and factor it with the pattern a² − b² = (a + b)(a − b). Factor the expression 4x^2 - 25 completely. Nice work — you factored a difference of squares from the ground up. Keep these moves in mind: Recognize the pattern: two perfect squares separated by subtraction. Identify the base terms: factor out what is being squared — here 2x and 5 , not 4x and 25 . Apply the formula: a^2 - b^2 = (a + b)(a - b) . Result: 4x^2 - 25 = (2x + 5)(2x - 5) . This pattern shows up constantly — watch for subtraction between squared terms like x^2 - 16 , 9x^2 - 49 , or 25x^2 - 1 . (Note: a SUM of squares like 4x^2 + 25 does not factor over the real numbers.)

This is the written version of the interactive lesson above. See the full Algebra 1 course.