EJERCICIO 22

176. a –b de b –a

B –a

+b –a

+2b -2ª

177. x –y de 2x +3y

2x +3y

-x  +y

+1x +4y

178. -5ª +b de -7ª +5

-7ª +5

+5ª       +b

-2ª +5 +b

179. x2 -5x de –x2 +6

-x2 +6

+x2       +5x

0 +6 +5x

180. x3 –xy2 de x2y +5xy2

X2y +5xy2

       +xy2 –x3

X2y +6xy2 –x3

181. 6ª2b -8ª3 de 7ª2b +5ab2

7ª2b +5ab2

-6ª2b          +8ª3

+1ª2b +5ab2 +8ª3

182. a –b +2c de –a +2b -3c

-a +2b -3c

-a +b -2c

-2ª +3b -5c

183. m –n +p de -3n +4m +5p

-3n +4m +5p

+n –m –p

-2n +3m +4p

184. –x +y -2 de x +3y -62

-62 +3y x

+2 –y +x

-52 +2y +2x

185. 3ª2 +ab -6b2 de -5b2 +8ab +a2

-5b2 +8ab +a2

+6b2 –ab -3ª2

+1b2 +7ab -2ª2

186. m2 –n2 -3mn de -5m2 –n2 +6mn

-5m2 –n2 +6mn

-m2 +n2 +3mn

-6m2 0 +9mn

187. –x3 –x +6 de -8x2 +5x -4

-8x2 +5x -4

         +x   -6 +x3

-8x2 +6x -10 +x3

188. m3 +14m2 +9 de 14m2 -8n +16

14m2 -8n +16

-14m2      -9 –m3

0 -8n +7 –m3

189. ab –bc +6cd de 8ab +5bc +6cd

8ab +5bc +6cd

-ab +bc -6cd

+7ab +6bc o        

190. 25a2b -8ab2 –b3 de a3 -9a2b –b3

A3 -9ª2b –b3

     -25ª2b +b3 +8ab2

A3 -34ª2b 0 +8ab2

191. xy2 -6y3 +4 de 6x3 -8x2y -6xy2

6x3 -8x2y -6xy2

                   -xy2 -4 +6y3

6x3 -8x2y -7xy2 -4 +6y3

192. m2 +7n -8c +d de m2 -9n +11c +14

M2 -9n +11c +14

-m2 -7n +8c       -d

0 -16n +19c +14 –d

193. 7ª3b +5ab2 -8ª2b2 +b4 de 5ª4 +9ª3b -40ab4 +6b4

5ª4 +9ª3b -40ab4 +6b4

      -7ª3b                -b4 -5ab3+8ª2b2

5ª4 +2ª3b -40ab4 +5b4 -5ab3 +8ª2b2

194. 6x3 -9x +6x2 -7 de x5 -8x4 +25x2 +15

X5 -8x4 +25x2 +15

              -6 x2   +7 +9x -6x3

X5 -8x4 +19x2 +22 +9y -6x3

195. x5 –x2y3 +6xy4 +25y5 de -3xy4 -8x3y2 -19y5 +18

-3xy4 -8x3y2 -19y5 +18

-6xy4       -25y5   -x5 +x2y3

-9xy4 -8x3y2 -44y5 +18 –x5 +x2y3

196. 25x +25x3 -18x2 -11x5 -46 de x3 -6x4 +8x2 -9 +15x

X3 -6x4 8x2 -9 +15x

-25x3     +18x2 +46 -25x +11x5

-24x3 -6x4 +26x2 +37 -10x +11x5

197. 23y3 +8y4 -15y5 -8y -5 de y6 +y3 +y2 +9

Y6 +y3 +y2 +9

    -23y3  +5 -8y4 +15y5 +8y

Y6 -22y3 +y2 +14 -8y4 +15y3 +8y

198. ax+2 -5ax+1 -6ax de ax+3 -8ax+1 -5

Ax+3 -8ax+1 -5

         +5ax+1       -ax+2 +6ax

Ax+3 -3ax+1 -5 –ax+2 -6ax

199. 8an-1 5an-2 +7an +an-3 de -8an +16an-4 +15an-2 +an-3

-8an +16an-4 +15an-2 +an-3

-7an              -5an-2 –an-3 -8an-1

-15an +16an-4 +10an-2 0 -8an-1

EJERCICIO 21

154. A +b restar a –b

A +b

-a +b

0 +2b

155. 2x -3y restar –x +2y

2x -3y

+x -2y

+3x -5y

156. 8ª +b restar -3ª +4

8ª +b

+3ª    +4

11ª +b +4

157. x2 -3x restar -5x +6

X2 -3x

      +5x +6

X2x2_____________________________________

 +2x +6

158. x –y +z restar x –y +z

X –y +z

-x +y –z

0   0    0

159. x +y –z restar –x –y +z

X +y –z

+x +y –z

+2x +2y -2z

160. x2 +y2 -3xy restar –y2 +3x2 -4xy

X2 +y2 -3xy

-3x2 +y2 +4xy

-2x2 +2y2 +1xy

161. x3 –x2 +6 restar 5x2 -4x +6

X3 –x2 +6

     -5x2 +6 -4x

X3 -6x2 +12 -4x

162. y2 +6y3 -8 restar 2y4 -3y2 +6y

Y2 +6y3 -8

+3y2            2y4 +6y

+4y2 +6y3 -8 2y4 +6y

163. a3 -6ab2 +9ª restar 15ª2b -8ª +5

A3 -6ab2 +9ª

               +8ª 15ª2b +5

A3 -6ab2 +17ª 15ª2b +5

164. x4 +9xy3 -11y4 restar -8x3y -6x2y2 +20y4

X4 +9xy3 -11y4

               -20y4 +8x3y -6x2y2

X4 +9xy3 -31y4 +8x3y -6x2y2

165. a +b +c –d restar –a –b +c –d

A +b +c –d

+a +b –c +d

+2ª +2b 0 0

166. ab +2ac -3cd -5de restar -4ac +8ab -5cd +5de

Ab +2ac -3cd -5de

-8ab +4ac +5cd -5de

-7ab +6ac +2cd -10de

167. X3 -9x +6x2 -19 restar -11x2 +21x -43 +6x3

X3 -9x +6x2 -19

-6x3 -21x +11x2 +43

5x3 -30x +17x2 +24

168. y5 -9y3 +6y2 -31 restar -11y4 +31y3 -8y2 -19y

Y5 -9y3 +6y2 -31

     -31y3 +8y2       +11y4 -19y

Y5 -40y3 +14y2 -31 +11y4 -19y

169. 15m3 -9n3 +6m2n -8mn2 restar 14mn2 -21m2n +5m3 -18

15m3 -9n3 +6m2n -8mn2

-5m3        +21m2n -14mn2 -18

+10m3 -9n3 +27m2n -22mn2 -18

170. 4x3y -19xy3 +y4 -6x2y2 restar –x4 -51xy3 +32x2y2 -25x3y

4x3y -19xy3 +y4 -6x2y2

+25x3y +32xy3    -32x2y2 +x4

+29x3y +32xy3 +y4 -38x2y2 +x4

171. m6 +m4n2 -9m2n4 +19 restar -13m3n3 +16mn5 -30m2n4 -61

M6 +m4n2 -9m2n4 +19

                +30m2n4 +61 +13m3n3 -16mn5

M6 +m4n2 +21m2n4 +80 +13m3n3 -16mn5

172. –a5b +6ª3b3 -18ab5 +42 restar -8ª6 +9b6 -11ª4b2 -11ª2b4

-a5b +6ª3b3 -18ab5 +42

                                      +8a6 -9b6 +11a4b2 +11a2b4

-a5b +6a3b3 -18ab5 +42 +8a6 -9b6 +11a4b2 +11a2b4

173. 1 –x2 +x4 –x3 +3x -6x5 restar –x6 +8x4 -30x2 +15x -24

1 –x2 +x4 –x3 +3x -6x5

+24 +30x2 -8x4     -15x       +x6

+25 +29x2 -7x4 –x3 -12x -6x5 +x6

174. ax +ax+1 –ax+2 restar 5ax -6ax+1 –ax+2

Ax +ax+1 –ax+2

-5ax +6ax+1 +ax+2

-4ax +7ax+1 0

175. ma –ma-1 +3ma—2 restar 3ma+1 -4ma +5ma-2 +8ma-3

Ma –ma-1 +3ma-2

+4ma -3ma+1 -2ma-2 -8ma-3

+5ma -4ma+1 -2ma-2 -8ma-3

Ejercicio 18

145. 1/2x2 +1/3xy, 1/2xy +1/4y2

1/2x2   +1/3xy

            1/2xy +1/4y2

1/2x2  1/6xy +1/4y2

146. a2 +1/2ab, -1/4ab +1/2b2, -1/4ab -1/5b2

a2 +1/2ab

     -1/4ab +1/2b2

    -1/4ab -1/5b2

a2 -0/32ab -3/10b2

147. x2 +2/3xy, -1/6xy +y2, -5/6xy +2/3y3

X2 +2/3xy

     -1/6xy +y2

    -5/6xy +2/3y2

X2 -5/15xy +1/3y2

148. 2/3a2 +1/5ab -1/2b2, 5/6a2 -1/10ab +1/6b2, -1/12a2 +1/20ab -1/8b2

2/3a2 +1/5ab -1/2b2

5/6a2 -1/10ab +1/6b2

-1/12a2 +1/20ab -1/3b2

243/21a2 +150/100ab -24/36b2

149. 3/4x2 -1/2y2, -2/5xy +1/6y2, 1/10xy +1/3y2

3/4x2 -1/2y2

          +1/6y2 -2/5xy

         +1/3y2 1/10xy

3/4x2 +24/36y2 +15/50xy

150. 5/6x2 -2/3y2 +3/4xy, -1/2xy -1/6x2 +1/8y2, 5/6xy -1/3x2 +1/4y2

5/6x2 -2/3y2 +3/4xy

        -1/6y2 -1/2xy

        +1/8y2

-1/3x2 +1/4y2 5/6xy

+9/8x2 +264/576y2 52/48xy

151. a3 -1/2ab2 +b3, 5/6ª2b -3/8ab2 -2b3, 1/4ª3 -1/2ª2b -3/5b3

a3 -1/2ab2 +b3

    -3/8ab2 -2b3 5/6a2b

1/4a3        -3/5b3 -1/2a2b

3/4a3 -2/16ab2 -1/10b3 +4/12a2b

152. x4 –x2 +5, 2/3x3 -3/8x -3, -3/5x4 +5/6x3 -3/4x

X4          –x2 +5

                      -3 2/3x3   -3/8x

-3/5x4               +5/6x3 -3/4x

-2/5x4 –x2 +2 +3/8x3 -12/32x

153. 2/3m3 -1/4mn2 +2/5n3, 1/6m2n +1/8mn2 -3/5n3, m3 -1/2, n –n3

2/3m3 -1/4mn2 +2/5n3

           +1/8mn2 -3/5n3 1/6m2n

m3                                              -1/2

                             n3                           n

1/3m3 +4/32mn2 -30n3 1/6m2n - 1/2  n

154. x4 +2x2y2 +2/7y4, -5/6x4 +3/8x2y2 -1/6xy3 -1/14y4, 5/6x3y -1/4x2y2 +1/7y4

X4 +2x2y2 +2/7y4

-5/6x4 +3/8x2y2 -1/4y4 -1/6xy3

       -1/4x2y2 +1/7y4                    5/6x3y

+1/6x4 +72/64x2y2 +35/196y4 -1/6xy2 5/6x3

Ejercicio 17

118. x2 +4x, -5x +x2

X2   +4x

+x2  -5x

0             -1x

119. a2 +ab, -2ab +b2

a2 +ab

b2 -2ab

0          -1ab

120. x3 +2x, -x2 +4

X3 +2x

            -x2 +4

X3 +2x -2x +4

121. a4 -3a2, a3 +4a

a4 -3a2

a3 +4ª

0     -1a

122. –x2 -4x, 7x +6, 3x2 -5

-x2 -4x

      -7x +6

3x2      -5

+2x2 -11x +1

123. –x2 +3x, x3 +6

-x2 +3x

            X3 +6

-x2 +3x x3 +6

124. m2 +n2, -3mn +4n2, -5m2 -5n2

m2 +n2

     +4n2 -3mn

-5m2 -5n2

-4m2 0 -3mn

125. 3x +x3, -4x2 +5, -x3 +4x2 -6

3x +x3

          -4x2 +5

    -x3 +4x2 -6

3x  0     0     -1

126. x2 -3xy +y2, -2y2 +3xy –x2, x2 +3xy –y2

X2 -3xy +y2

-x2 +3xy -2y2

X2 +3xy –y2

1x2 +3xy -2y2

127. a2 -3ab +b2

+a2 -5ab –b2

-2a2 8ab –b2

0    0      -1b2

128. -7x2 +5x -6, 8x -9 +4x2, -7x +14 –x2

-7x2 +5x -6

+4x2 8x -9

-x2 -7x +14

-4x2 +6x -1

129. –x2 +x -6, x3 -7x2 +5, -x3 +8x -5

-x2     +x   -6

-7x2           +5 x3

         +8x   -5 –x3

-8x2 +9x    -6    0

130. a3 –b3, 5a2b -4ab2, a3 -7ab2 –b3

a3     -b3

                    5a2b -4ab2

a3   -b3                 -7ab2

0      0    5a2b     11ab2

131. x3 +xy2 +y3, -5x2y +x3 –y3, 2x3 -4xy2 -5y3

X3 +xy2 +y3

+x3        -y3 -5x2y

2x3 -4xy2 -5y3

+4x3 -3xy2 -5y3 -5x2y

132. -732n +4n3, m3 +6mn2 –n3, -m3 +7m2n +5n3

-7m2n +4n3

                     m3 +6mn2 –n3

+7m2n +5n3  -m3

O +9n3 0 +6mn2 –n3

133. x4 –x2 +x, x3 -4x2 +5, 7x2 -4x +6

X4  -x2  +x

      -4x2      x3   +5

     7x2      -4x  +6

X4  -2x2  -3x  x3  +11

134. a4 +a6 +6, a5 -3ª3 +8, a3 –a2 -14

a4  +a6  +6

             +8  a5  -3a3

            -14          a3    -a2

a4  +a6  0  a5  -2a3  -a2

135. x5 +x -9, 3x4 -7x2 +6, -3x3 -4x +5

X5  +x  -9

            +6  3x4  -7x2

    -4x  +5  -3x3  -7x2

X5  -3x +2    0    -7x2

136. a3 +a, a2 +5, 7ª2 +4ª, -8ª2 -6

a3  +a

             a2  +5

   +4a  -7a2 

           -8a2     -6

 a3         +5a o  -1

137. x4 –x2y2, -5x3y +6xy3, -4xy3 +y4, -4x2y2 -6

X4  -x2y2

                   -5x3y  +6xy3

                              -4xy3  +y4

     -4x2y2                                 -6

X4 -5x2y2 -5x3y   +2xy3 +y4    -6

138. xy +x2, -7y2 +4xy +4xy –x3, 5x2 –x2 +6xy, -6x2 -4xy +y2

 Xy   +x2

+4xy –x2 -7y2

+6xy 5x2 +y2

-4xy –x2

     -6x2

+5xy -2x2 -6y2

139. a3 -8ax2 +x3, 5a2x -6a2x –x3, -4a3 +4a2m -3am2, 7a2m -4am2 -6

a3 -8ax2 +x3

     -6ax2 –x3    5a2x

3a3          -x3  -5a2x

a3 +14ax2 –x3

5a3 0 -2x3 0

140. -8ª2m +6am2 –m, a3 -5am2 +m3, -4ª3 +4ª2m -3am2, 7ª2m -4am2 -6

-8a2m +6am2 –m3

           -5am2 +m3 a3

+4a2m -3am2        -4a3

          -4ax2                  -6

-4a2m -6am2 0   -3a3 -6

141. a5 +a6 +a2, a4 +a3 +6, 3a2 +5a -8, -5a -4a2 -5a +6

a5 +a6 +a2

                 a4 +a3 +6

           3a2           -8 +5a

-a5    -4a2           +6 -5a

0 +a6    0 a4 +a3 +4     0

142. m3 –n3 +6m2n, -4m2n +5mn2 +n3, m3 –n3 +6mn2, -2m3 -2m2n +n3

m3 –n3 +6m2n

     +n3 -4m2n +5mn2

m3 –n3           +6mn2

-2m3 +n3 -2m2n

0    0     0       +11mn2

143. ax -3ax-2, 5ax-1 +6ax-3, 7ax-3 +ax-4, ax-1 -13ax-3

ax -3ax-2

                 5ax-1 +6ax-3

                            7ax-3      +a4-4

                Ax-1    -13ax-3

ax -3ax-2 6ax-1    0            +a4-4

144. ax+2 –ax +ax+1, -3ax+3 –ax-1 +ax-2, ax +4ax+4 -5ax+2, ax-1 –ax-2 +ax+2

Ax+2        –ax   +ax+1

+ax+2              -ax+1      3ax+3

-5ax+2     ax                  +4ax+3

                       ax-1

                     -ax-2

                     +ax+2

-3ax+2 0     +1ax+2      +1ax+3