factor 16x^3-2

{ "query": { "display": "factor $$16x^{3}-2$$", "symbolab_question": "FACTOR#factor 16x^{3}-2" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Algebra", "subTopic": "Simplify", "default": "2(2x-1)(4x^{2}+2x+1)", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Factor $$16x^{3}-2:{\\quad}2\\left(2x-1\\right)\\left(4x^{2}+2x+1\\right)$$", "input": "16x^{3}-2", "steps": [ { "type": "interim", "title": "Factor out common term $$2:{\\quad}2\\left(8x^{3}-1\\right)$$", "input": "16x^{3}-2", "steps": [ { "type": "step", "primary": "Rewrite $$16$$ as $$2\\cdot\\:8$$", "secondary": [ "Rewrite $$2$$ as $$2\\cdot\\:1$$" ], "result": "=2\\cdot\\:8x^{3}-2\\cdot\\:1" }, { "type": "step", "primary": "Factor out common term $$2$$", "result": "=2\\left(8x^{3}-1\\right)", "meta": { "practiceLink": "/practice/factoring-practice", "practiceTopic": "Factoring" } } ], "meta": { "solvingClass": "Solver2", "interimType": "Factor Take Out Common Term Title 1Eq" } }, { "type": "step", "result": "=2\\left(8x^{3}-1\\right)" }, { "type": "interim", "title": "Factor $$8x^{3}-1:{\\quad}\\left(2x-1\\right)\\left(2^{2}x^{2}+2x+1\\right)$$", "input": "8x^{3}-1", "steps": [ { "type": "interim", "title": "Apply exponent rules", "input": "8x^{3}-1", "steps": [ { "type": "step", "primary": "Rewrite $$8$$ as $$2^{3}$$", "result": "=2^{3}x^{3}-1" }, { "type": "step", "primary": "Rewrite $$1$$ as $$1^{3}$$", "result": "=2^{3}x^{3}-1^{3}" }, { "type": "step", "primary": "Apply exponent rule: $$a^{m}b^{m}=\\left(ab\\right)^{m}$$", "secondary": [ "$$2^{3}x^{3}=\\left(2x\\right)^{3}$$" ], "result": "=\\left(2x\\right)^{3}-1^{3}", "meta": { "practiceLink": "/practice/exponent-practice", "practiceTopic": "Expand FOIL" } } ], "meta": { "interimType": "Apply Exp Rules Title 0Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7PvaI9YhsyEYN5HkVnzcx4b1s8XGd9YWXhOv9apLWtv25jaeBHPl8nHswcQQZVfVHsVBV2q+3sRfeqjWHFfpgTrcjn1IXHK8TdnN3z07KH5ezerCcKpz95cmOAqetMMtLqpCF+pLHginRLYfnCC58Mg48m+omseXNXglDeFISMfbnGcX57Hy3fYoom/ZxpK5G" } }, { "type": "step", "result": "=\\left(2x\\right)^{3}-1^{3}" }, { "type": "step", "primary": "Apply Difference of Cubes Formula: $$x^{3}-y^{3}=\\left(x-y\\right)\\left(x^{2}+xy+y^{2}\\right)$$", "secondary": [ "$$\\left(2x\\right)^{3}-1^{3}=\\left(2x-1\\right)\\left(2^{2}x^{2}+2x+1\\right)$$" ], "result": "=\\left(2x-1\\right)\\left(2^{2}x^{2}+2x+1\\right)", "meta": { "practiceLink": "/practice/factoring-practice#area=main&subtopic=Sum%2FDifference%20of%20Cubes", "practiceTopic": "Factor Difference of Cubes" } } ], "meta": { "solvingClass": "Solver2", "interimType": "Generic Factor Specific 1Eq" } }, { "type": "step", "result": "=2\\left(2x-1\\right)\\left(2^{2}x^{2}+2x+1\\right)" }, { "type": "step", "primary": "$$2^{2}=4$$", "result": "=2\\left(2x-1\\right)\\left(4x^{2}+2x+1\\right)" } ], "meta": { "solvingClass": "Solver2" } }, "meta": { "showVerify": true } }