{
"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": "Factorizar $$x^{2}-225y^{2}:{\\quad}\\left(x+15y\\right)\\left(x-15y\\right)$$",
"input": "x^{2}-225y^{2}",
"steps": [
{
"type": "interim",
"title": "Simplificar $$225y^{2}:{\\quad}\\left(15y\\right)^{2}$$",
"input": "225y^{2}",
"steps": [
{
"type": "step",
"primary": "Descomponer el número en factores primos: $$225=15^{2}$$",
"result": "=15^{2}y^{2}"
},
{
"type": "step",
"primary": "Aplicar las leyes de los exponentes: $$a^{n}b^{n}=\\left(a\\cdot\\:b\\right)^{n}$$",
"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/sw8Nt2sXXQchKWGMl7zPLrmINtymggwJLd1ohke2Wgml78++2zI0g=="
}
},
{
"type": "step",
"result": "=x^{2}-\\left(15y\\right)^{2}"
},
{
"type": "step",
"primary": "Aplicar la siguiente regla para binomios al cuadrado: $$x^{2}-y^{2}=\\left(x+y\\right)\\left(x-y\\right)$$",
"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
}
}
Solución
factor
Solución
Pasos de solución
Simplificar
Aplicar la siguiente regla para binomios al cuadrado: