factor x^2-225y^2

{ "query": { "display": "factor $$x^{2}-225y^{2}$$", "symbolab_question": "FACTOR#factor x^{2}-225y^{2}" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Algebra", "subTopic": "Simplify", "default": "(x+15y)(x-15y)", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Factor $$x^{2}-225y^{2}:{\\quad}\\left(x+15y\\right)\\left(x-15y\\right)$$", "input": "x^{2}-225y^{2}", "steps": [ { "type": "interim", "title": "Simplify $$225y^{2}:{\\quad}\\left(15y\\right)^{2}$$", "input": "225y^{2}", "steps": [ { "type": "step", "primary": "Factor the number: $$225=15^{2}$$", "result": "=15^{2}y^{2}" }, { "type": "step", "primary": "Apply exponent rule: $$a^{n}b^{n}=\\left(a\\cdot\\:b\\right)^{n}$$", "secondary": [ "$$15^{2}y^{2}=\\left(15y\\right)^{2}$$" ], "result": "=\\left(15y\\right)^{2}", "meta": { "practiceLink": "/practice/exponent-practice", "practiceTopic": "Expand FOIL" } } ], "meta": { "solvingClass": "Solver2", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7JFpMXdM8IkAYU3d+QvNyUs0ag8T1MwTer44+aCS/ZFBi9bNMcsvIcWcD/fHG2hXYP8vQyhiD4JSfqjIvcQ7timkSOxgqdB0M/sw8Nt2sXXRaA50b8EhCY9tlee5vjy7K" } }, { "type": "step", "result": "=x^{2}-\\left(15y\\right)^{2}" }, { "type": "step", "primary": "Apply Difference of Two Squares Formula: $$x^{2}-y^{2}=\\left(x+y\\right)\\left(x-y\\right)$$", "secondary": [ "$$x^{2}-\\left(15y\\right)^{2}=\\left(x+15y\\right)\\left(x-15y\\right)$$" ], "result": "=\\left(x+15y\\right)\\left(x-15y\\right)", "meta": { "practiceLink": "/practice/factoring-practice#area=main&subtopic=Difference%20of%20Two%20Squares", "practiceTopic": "Factor Difference of Squares" } } ], "meta": { "solvingClass": "Solver2" } }, "meta": { "showVerify": true } }