Question

Resuelve las siguientes multiplicaciones

A (5m – 3mn + 6n) (mn – 7m + 3n)

B (2x3+ 9x2- 5x + 1) (6x2+ 7x3- 8x – 5)

C (2ab – 4bc +2ac) (7ab – ac + 9bc)



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Answer 1

(5m−3mn+6n)(mn−7m+3n)

=(5m+−3mn+6n)(mn+−7m+3n)

=(5m)(mn)+(5m)(−7m)+(5m)(3n)+(−3mn)(mn)+(−3mn)(−7m)+(−3mn)(3n)+(6n)(mn)+(6n)(−7m)+(6n)(3n)

=5m2n−35m2+15mn−3m2n2+21m2n−9mn2+6mn2−42mn+18n2

=−3m2n2+26m2n−3mn2−35m2−27mn+18n2

(2x3+9x2−5x+1)(6x2+7x3−8x−5)

=(2x3+9x2+−5x+1)(6x2+7x3+−8x+−5)

=(2x3)(6x2)+(2x3)(7x3)+(2x3)(−8x)+(2x3)(−5)+(9x2)(6x2)+(9x2)(7x3)+(9x2)(−8x)+(9x2)(−5)+(−5x)(6x2)+(−5x)(7x3)+(−5x)(−8x)+(−5x)(−5)+(1)(6x2)+(1)(7x3)+(1)(−8x)+(1)(−5)

=12x5+14x6−16x4−10x3+54x4+63x5−72x3−45x2−30x3−35x4+40x2+25x+6x2+7x3−8x−5

=14x6+75x5+3x4−105x3+x2+17x−5

(2ab−4bc+2ac)(7ab−ac+9bc)

=(2ab+−4bc+2ac)(7ab+−ac+9bc)

=(2ab)(7ab)+(2ab)(−ac)+(2ab)(9bc)+(−4bc)(7ab)+(−4bc)(−ac)+(−4bc)(9bc)+(2ac)(7ab)+(2ac)(−ac)+(2ac)(9bc)

=14a2b2−2a2bc+18ab2c−28ab2c+4abc2−36b2c2+14a2bc−2a2c2+18abc2

=14a2b2+12a2bc−2a2c2−10ab2c+22abc2−36b2c2