{
"query": {
"display": "factor $$4x^{3}a^{5}m^{6}-2x^{3}a^{5}m^{7}-16a^{6}$$",
"symbolab_question": "FACTOR#factor 4x^{3}a^{5}m^{6}-2x^{3}a^{5}m^{7}-16a^{6}"
},
"solution": {
"level": "PERFORMED",
"subject": "Algebra",
"topic": "Algebra",
"subTopic": "Simplify",
"default": "2a^{5}(2x^{3}m^{6}-x^{3}m^{7}-8a)",
"meta": {
"showVerify": true
}
},
"steps": {
"type": "interim",
"title": "Factorizar $$4x^{3}a^{5}m^{6}-2x^{3}a^{5}m^{7}-16a^{6}:{\\quad}2a^{5}\\left(2x^{3}m^{6}-x^{3}m^{7}-8a\\right)$$",
"input": "4x^{3}a^{5}m^{6}-2x^{3}a^{5}m^{7}-16a^{6}",
"steps": [
{
"type": "interim",
"title": "Factorizar el termino común $$2a^{5}:{\\quad}2a^{5}\\left(2x^{3}m^{6}-x^{3}m^{7}-8a\\right)$$",
"input": "4x^{3}a^{5}m^{6}-2x^{3}a^{5}m^{7}-16a^{6}",
"steps": [
{
"type": "interim",
"title": "Factorizar el termino común $$2:{\\quad}2\\left(2x^{3}a^{5}m^{6}-x^{3}a^{5}m^{7}-8a^{6}\\right)$$",
"input": "4x^{3}a^{5}m^{6}-2x^{3}a^{5}m^{7}-16a^{6}",
"steps": [
{
"type": "interim",
"title": "$$4x^{3}a^{5}m^{6}=2\\cdot\\:2x^{3}a^{5}m^{6}$$",
"input": "4x^{3}a^{5}m^{6}",
"steps": [
{
"type": "step",
"primary": "Descomponer el número en factores primos: $$4=2\\cdot\\:2$$",
"result": "=2\\cdot\\:2x^{3}a^{5}m^{6}"
}
],
"meta": {
"interimType": "N/A"
}
},
{
"type": "interim",
"title": "$$16a^{6}=2\\cdot\\:8a^{6}$$",
"input": "16a^{6}",
"steps": [
{
"type": "step",
"primary": "Descomponer el número en factores primos: $$16=2\\cdot\\:8$$",
"result": "=2\\cdot\\:8a^{6}"
}
],
"meta": {
"interimType": "N/A"
}
},
{
"type": "step",
"result": "=2\\cdot\\:2x^{3}a^{5}m^{6}-2x^{3}a^{5}m^{7}-2\\cdot\\:8a^{6}"
},
{
"type": "step",
"primary": "Factorizar el termino común $$2$$",
"result": "=2\\left(2x^{3}a^{5}m^{6}-x^{3}a^{5}m^{7}-8a^{6}\\right)",
"meta": {
"practiceLink": "/practice/factoring-practice",
"practiceTopic": "Factoring"
}
}
],
"meta": {
"solvingClass": "Solver2",
"interimType": "Factor Take Out Common Term Title 1Eq"
}
},
{
"type": "step",
"result": "=2\\left(2x^{3}a^{5}m^{6}-x^{3}a^{5}m^{7}-8a^{6}\\right)"
},
{
"type": "interim",
"title": "Factorizar el termino común $$a^{5}:{\\quad}a^{5}\\left(2x^{3}m^{6}-x^{3}m^{7}-8a\\right)$$",
"input": "2x^{3}a^{5}m^{6}-x^{3}a^{5}m^{7}-8a^{6}",
"steps": [
{
"type": "step",
"primary": "Aplicar las leyes de los exponentes: $$a^{b+c}=a^b\\cdot\\:a^c$$",
"secondary": [
"$$a^{6}=a^{5}a$$"
],
"result": "=2x^{3}a^{5}m^{6}-x^{3}a^{5}m^{7}-8a^{5}a",
"meta": {
"practiceLink": "/practice/exponent-practice",
"practiceTopic": "Expand FOIL"
}
},
{
"type": "step",
"primary": "Factorizar el termino común $$a^{5}$$",
"result": "=a^{5}\\left(2x^{3}m^{6}-x^{3}m^{7}-8a\\right)",
"meta": {
"practiceLink": "/practice/factoring-practice",
"practiceTopic": "Factoring"
}
}
],
"meta": {
"solvingClass": "Solver2",
"interimType": "Factor Take Out Common Term Title 1Eq"
}
},
{
"type": "step",
"result": "=2a^{5}\\left(2x^{3}m^{6}-x^{3}m^{7}-8a\\right)"
}
],
"meta": {
"solvingClass": "Solver2",
"interimType": "Factor Take Out Common Term Title 1Eq"
}
},
{
"type": "step",
"result": "=2a^{5}\\left(2x^{3}m^{6}-x^{3}m^{7}-8a\\right)"
}
],
"meta": {
"solvingClass": "Solver2"
}
},
"meta": {
"showVerify": true
}
}
Solución
factor
Solución
Pasos de solución
Factorizar el termino común