factor 16-x^4

{ "query": { "display": "factor $$16-x^{4}$$", "symbolab_question": "FACTOR#factor 16-x^{4}" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Algebra", "subTopic": "Simplify", "default": "-(x^{2}+4)(x+2)(x-2)", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Factor $$16-x^{4}:{\\quad}-\\left(x^{2}+4\\right)\\left(x+2\\right)\\left(x-2\\right)$$", "input": "16-x^{4}", "steps": [ { "type": "step", "primary": "Write in the standard form ", "result": "=-x^{4}+16" }, { "type": "interim", "title": "Factor out $$-1:{\\quad}-\\left(x^{4}-16\\right)$$", "input": "-x^{4}+16", "steps": [ { "type": "step", "primary": "Rewrite $$16$$ as $$-\\left(-16\\right)$$", "result": "=-x^{4}-\\left(-16\\right)" }, { "type": "step", "primary": "Factor out $$-1$$", "result": "=-\\left(x^{4}-16\\right)" } ], "meta": { "solvingClass": "Solver2", "interimType": "Factor Out Specific 1Eq" } }, { "type": "step", "result": "=-\\left(x^{4}-16\\right)" }, { "type": "interim", "title": "Factor $$x^{4}-16:{\\quad}\\left(x^{2}+4\\right)\\left(x+2\\right)\\left(x-2\\right)$$", "input": "x^{4}-16", "steps": [ { "type": "interim", "title": "Apply exponent rules", "input": "x^{4}-16", "steps": [ { "type": "step", "primary": "Rewrite $$16$$ as $$4^{2}$$", "result": "=x^{4}-4^{2}" }, { "type": "step", "primary": "Apply exponent rule: $$a^{bc}=\\left(a^{b}\\right)^{c}$$", "secondary": [ "$$x^{4}=\\left(x^{2}\\right)^{2}$$" ], "result": "=\\left(x^{2}\\right)^{2}-4^{2}", "meta": { "practiceLink": "/practice/exponent-practice", "practiceTopic": "Expand FOIL" } } ], "meta": { "interimType": "Apply Exp Rules Title 0Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7rWc4RN6B6znLT0mHLvlet2ncaYaF/MDtqlipp6yOsOu5jaeBHPl8nHswcQQZVfVHsVBV2q+3sRfeqjWHFfpgTvJVY6OuG6k2+UcrkOPfatuLURIVsFgWop4y6tyqyinO1sD7NfhsPe7eDHrmjY0mE9IlGhTocLpuLor5cjpkiIgcVBYWZA09tgc0INvET0Hn" } }, { "type": "step", "result": "=\\left(x^{2}\\right)^{2}-4^{2}" }, { "type": "step", "primary": "Apply Difference of Two Squares Formula: $$x^{2}-y^{2}=\\left(x+y\\right)\\left(x-y\\right)$$", "secondary": [ "$$\\left(x^{2}\\right)^{2}-4^{2}=\\left(x^{2}+4\\right)\\left(x^{2}-4\\right)$$" ], "result": "=\\left(x^{2}+4\\right)\\left(x^{2}-4\\right)", "meta": { "practiceLink": "/practice/factoring-practice#area=main&subtopic=Difference%20of%20Two%20Squares", "practiceTopic": "Factor Difference of Squares" } }, { "type": "interim", "title": "Factor $$x^{2}-4:{\\quad}\\left(x+2\\right)\\left(x-2\\right)$$", "input": "x^{2}-4", "steps": [ { "type": "step", "primary": "Rewrite $$4$$ as $$2^{2}$$", "result": "=x^{2}-2^{2}" }, { "type": "step", "primary": "Apply Difference of Two Squares Formula: $$x^{2}-y^{2}=\\left(x+y\\right)\\left(x-y\\right)$$", "secondary": [ "$$x^{2}-2^{2}=\\left(x+2\\right)\\left(x-2\\right)$$" ], "result": "=\\left(x+2\\right)\\left(x-2\\right)", "meta": { "practiceLink": "/practice/factoring-practice#area=main&subtopic=Difference%20of%20Two%20Squares", "practiceTopic": "Factor Difference of Squares" } } ], "meta": { "solvingClass": "Solver2", "interimType": "Generic Factor Specific 1Eq" } }, { "type": "step", "result": "=\\left(x^{2}+4\\right)\\left(x+2\\right)\\left(x-2\\right)" } ], "meta": { "solvingClass": "Solver2", "interimType": "Generic Factor Specific 1Eq" } }, { "type": "step", "result": "=-\\left(x^{2}+4\\right)\\left(x+2\\right)\\left(x-2\\right)" } ], "meta": { "solvingClass": "Solver2" } }, "meta": { "showVerify": true } }