factor 4x^3a^5m^6-2x^3a^5m^7-16a^6

{ "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": "Factor $$4x^{3}a^{5}m^{6}-2x^{3}a^{5}m^{7}-16a^{6}:{\\quad}2a^{5}\\left(2x^{3}m^{6}-x^{3}m^{7}-8a\\right)$$", "input": "4x^{3}a^{5}m^{6}-2x^{3}a^{5}m^{7}-16a^{6}", "steps": [ { "type": "interim", "title": "Factor out common term $$2a^{5}:{\\quad}2a^{5}\\left(2x^{3}m^{6}-x^{3}m^{7}-8a\\right)$$", "input": "4x^{3}a^{5}m^{6}-2x^{3}a^{5}m^{7}-16a^{6}", "steps": [ { "type": "interim", "title": "Factor out common term $$2:{\\quad}2\\left(2x^{3}a^{5}m^{6}-x^{3}a^{5}m^{7}-8a^{6}\\right)$$", "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": "Factor the number: $$4=2\\cdot\\:2$$", "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": "Factor the number: $$16=2\\cdot\\:8$$", "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": "Factor out common term $$2$$", "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": "Factor out common term $$a^{5}:{\\quad}a^{5}\\left(2x^{3}m^{6}-x^{3}m^{7}-8a\\right)$$", "input": "2x^{3}a^{5}m^{6}-x^{3}a^{5}m^{7}-8a^{6}", "steps": [ { "type": "step", "primary": "Apply exponent rule: $$a^{b+c}=a^b\\cdot\\:a^c$$", "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": "Factor out common term $$a^{5}$$", "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 } }