Respuestas
Respuesta dada por:
3
Bueno vamos a usar éstos casos de factoreo,,,
![ad+cd+(a+c) \\ d(a+c)+(a+c) \\ (a+c)(d+1) ad+cd+(a+c) \\ d(a+c)+(a+c) \\ (a+c)(d+1)](https://tex.z-dn.net/?f=ad%2Bcd%2B%28a%2Bc%29+%5C%5C+d%28a%2Bc%29%2B%28a%2Bc%29+%5C%5C+%28a%2Bc%29%28d%2B1%29)
Ahora empecemos:
![i) \\ 2a^{2} -4ab-5a+10b \\ (2 a^{2}-4ab )+(-5a+10b) \\ 2a(a-2b)-5(a-2b) \\ (a-2b)(2a-5) \\ \\ ii) \\ 7a b^{2} +ac-14b^{2} xy-2cxy \\ (7a b^{2} -14b^{2} xy)+(ac-2cxy) \\ 7 b^{2} (a-2xy)+c(a-2xy) \\ (a-2xy)(7 b^{2}+c ) \\ \\ iii) \\ x^{2} y^{3} +5y^{3}-3 x^{2} -15 \\ (x^{2} y^{3}-3 x^{2} )+(5y^{3}-15) \\ x^{2} ( y^{3} -3)+5(y^{3} -3) \\ ( y^{3}-3 )(x^{2} +5) \\ \\ iv) \\ 5ab-10-5x-abc^{2} +2 c^{2} + c^{2} x \\ (5ab-10-5x)+(-abc^{2}+2 c^{2}+ c^{2}x ) \\ 5(ab-2-x)- c^{2} (ab-2-x) \\ (ab-2-x)(5-c^{2} ) i) \\ 2a^{2} -4ab-5a+10b \\ (2 a^{2}-4ab )+(-5a+10b) \\ 2a(a-2b)-5(a-2b) \\ (a-2b)(2a-5) \\ \\ ii) \\ 7a b^{2} +ac-14b^{2} xy-2cxy \\ (7a b^{2} -14b^{2} xy)+(ac-2cxy) \\ 7 b^{2} (a-2xy)+c(a-2xy) \\ (a-2xy)(7 b^{2}+c ) \\ \\ iii) \\ x^{2} y^{3} +5y^{3}-3 x^{2} -15 \\ (x^{2} y^{3}-3 x^{2} )+(5y^{3}-15) \\ x^{2} ( y^{3} -3)+5(y^{3} -3) \\ ( y^{3}-3 )(x^{2} +5) \\ \\ iv) \\ 5ab-10-5x-abc^{2} +2 c^{2} + c^{2} x \\ (5ab-10-5x)+(-abc^{2}+2 c^{2}+ c^{2}x ) \\ 5(ab-2-x)- c^{2} (ab-2-x) \\ (ab-2-x)(5-c^{2} )](https://tex.z-dn.net/?f=i%29+%5C%5C+2a%5E%7B2%7D+-4ab-5a%2B10b+%5C%5C+%282+a%5E%7B2%7D-4ab+%29%2B%28-5a%2B10b%29+%5C%5C+2a%28a-2b%29-5%28a-2b%29+%5C%5C+%28a-2b%29%282a-5%29+%5C%5C++%5C%5C+ii%29+%5C%5C+7a+b%5E%7B2%7D+%2Bac-14b%5E%7B2%7D+xy-2cxy+%5C%5C+%287a+b%5E%7B2%7D+-14b%5E%7B2%7D+xy%29%2B%28ac-2cxy%29+%5C%5C+7+b%5E%7B2%7D+%28a-2xy%29%2Bc%28a-2xy%29+%5C%5C+%28a-2xy%29%287+b%5E%7B2%7D%2Bc+%29+%5C%5C++%5C%5C+iii%29++%5C%5C+x%5E%7B2%7D++y%5E%7B3%7D+%2B5y%5E%7B3%7D-3+x%5E%7B2%7D+-15+%5C%5C+%28x%5E%7B2%7D++y%5E%7B3%7D-3+x%5E%7B2%7D+%29%2B%285y%5E%7B3%7D-15%29+%5C%5C++x%5E%7B2%7D+%28+y%5E%7B3%7D+-3%29%2B5%28y%5E%7B3%7D+-3%29+%5C%5C+%28+y%5E%7B3%7D-3+%29%28x%5E%7B2%7D+%2B5%29+%5C%5C++%5C%5C+iv%29+%5C%5C+5ab-10-5x-abc%5E%7B2%7D+%2B2+c%5E%7B2%7D+%2B+c%5E%7B2%7D+x+%5C%5C+%285ab-10-5x%29%2B%28-abc%5E%7B2%7D%2B2+c%5E%7B2%7D%2B+c%5E%7B2%7Dx++%29+%5C%5C+5%28ab-2-x%29-+c%5E%7B2%7D+%28ab-2-x%29+%5C%5C+%28ab-2-x%29%285-c%5E%7B2%7D+%29)
![v) \\ a^{2} x^{2} - b^{3} x^{2} + x^{2} - a^{2} bc+ b^{4} c-bc \\ (a^{2} x^{2} - b^{3} x^{2} + x^{2})+(- a^{2} bc+ b^{4} c-bc ) \\ x^{2} ( a^{2}- b^{3}+1 )-bc( a^{2}-b ^{3} +1 ) \\ ( a^{2}- b^{3}+1 )( x^{2} -bc) \\ \\ vi) \\ 3 a^{2} x-3 b^{2} x-3x- a^{2}+ b^{2} +1 \\ (3 a^{2} x-3 b^{2} x-3x)+(- a^{2}+ b^{2} +1) \\ 3x( a^{2}- b^{2} -1 )-( a^{2}- b^{2}-1 ) \\ ( a^{2}- b^{2}-1 )(3x-1) \\ \\ vii) \\ 10a-15b-20+6ax-9bx-12x \\ (10a-15b-20)+(6ax-9bx-12x) \\ 5(2a-3b-4)+3x(2a-3b-4) \\ (2a-3b-4)(5+3x) v) \\ a^{2} x^{2} - b^{3} x^{2} + x^{2} - a^{2} bc+ b^{4} c-bc \\ (a^{2} x^{2} - b^{3} x^{2} + x^{2})+(- a^{2} bc+ b^{4} c-bc ) \\ x^{2} ( a^{2}- b^{3}+1 )-bc( a^{2}-b ^{3} +1 ) \\ ( a^{2}- b^{3}+1 )( x^{2} -bc) \\ \\ vi) \\ 3 a^{2} x-3 b^{2} x-3x- a^{2}+ b^{2} +1 \\ (3 a^{2} x-3 b^{2} x-3x)+(- a^{2}+ b^{2} +1) \\ 3x( a^{2}- b^{2} -1 )-( a^{2}- b^{2}-1 ) \\ ( a^{2}- b^{2}-1 )(3x-1) \\ \\ vii) \\ 10a-15b-20+6ax-9bx-12x \\ (10a-15b-20)+(6ax-9bx-12x) \\ 5(2a-3b-4)+3x(2a-3b-4) \\ (2a-3b-4)(5+3x)](https://tex.z-dn.net/?f=v%29+%5C%5C++a%5E%7B2%7D++x%5E%7B2%7D+-+b%5E%7B3%7D++x%5E%7B2%7D+%2B+x%5E%7B2%7D+-+a%5E%7B2%7D+bc%2B+b%5E%7B4%7D+c-bc+%5C%5C+%28a%5E%7B2%7D++x%5E%7B2%7D+-+b%5E%7B3%7D++x%5E%7B2%7D+%2B+x%5E%7B2%7D%29%2B%28-+a%5E%7B2%7D+bc%2B+b%5E%7B4%7D+c-bc+%29+%5C%5C++x%5E%7B2%7D+%28+a%5E%7B2%7D-+b%5E%7B3%7D%2B1++%29-bc%28+a%5E%7B2%7D-b+%5E%7B3%7D+%2B1+%29+%5C%5C+%28+a%5E%7B2%7D-+b%5E%7B3%7D%2B1++%29%28+x%5E%7B2%7D+-bc%29+%5C%5C++%5C%5C+vi%29+%5C%5C+3+a%5E%7B2%7D+x-3+b%5E%7B2%7D+x-3x-+a%5E%7B2%7D%2B+b%5E%7B2%7D++%2B1+%5C%5C+%283+a%5E%7B2%7D+x-3+b%5E%7B2%7D+x-3x%29%2B%28-+a%5E%7B2%7D%2B+b%5E%7B2%7D++%2B1%29+%5C%5C+3x%28+a%5E%7B2%7D-+b%5E%7B2%7D+-1+%29-%28+a%5E%7B2%7D-+b%5E%7B2%7D-1++%29+%5C%5C+%28+a%5E%7B2%7D-+b%5E%7B2%7D-1++%29%283x-1%29+%5C%5C++%5C%5C+vii%29+%5C%5C+10a-15b-20%2B6ax-9bx-12x+%5C%5C+%2810a-15b-20%29%2B%286ax-9bx-12x%29+%5C%5C+5%282a-3b-4%29%2B3x%282a-3b-4%29+%5C%5C+%282a-3b-4%29%285%2B3x%29)
Y eso sería todo...espero te sirva y si tienes alguna duda me avisas
Nota: primero agrupamos los términos a nuestra conveniencia...y sacamos factor común...
Ahora empecemos:
Y eso sería todo...espero te sirva y si tienes alguna duda me avisas
Nota: primero agrupamos los términos a nuestra conveniencia...y sacamos factor común...
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