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

Ejercicio 16

96. 3a +2b –c, 2a +3b +c

 3a +2b –c

 2a+3b +c

5a +5b

97. m +n –p, -m-n +p

m  +n  –p

-m –n +p

     0

98. a +b –c, 2a +2b -2c, -3a –b +3c

a  +b  -c

2a +2b -2c

-3a –b +3c

     +2b

99. -7x -4x +6z, 10x -20y -8z, -5x +24y +2z

-7x -4x +6z

10x -20y -8z

-5x +24y +2z

+2x

100. -5a -2b -3c, 7a -3b +5c, -8a +5b -3c

-5a -2b -3c

7a -3b +5c

-8a +5b -3c

-6a        -1c

101. ax +by –az, -5ax -7ay -6az, 4ax +9ay +8az

ax +ay –az

-5ax -7ay -6az

4a +9ay +8az

0 +3ay +1az

102. –am +6mn -4s, 6s –am -5mn, -2s -5mn +3am

-am +6mn -4s

-am -5mn 6s

+3am -5mn -2s

+1am -4mn 0

103. 6m -3n, -4n +5p, -m -5p

6m -3n

     -4n +5p

-m       -5p

+5m -7n 0

104. 2x -3y, 5z +9, 6x -4, 3y -5

2x -3y

           5z +9

6x            -4

       3y -5

+8x 0 +5z 0

105. 7x +2y -4, 9y -6z +5, -y +3z -6, -5 +8x -3y

7x +2y -4

      9y +5 -6z

      -y -6 +3z

+8x -3y -5

15x +7y -10 -3z

106.5ax -3am -7an, -8ax +5am -9an, -11am +16an

5ax -3am -7an

-8ax +5am -9an

-11ax +5am -16an

-14ax +7am 0

107. 8x +y +z +u, -3x -4y -2z +3u, 4x +5y 63z -4u, -9x –y +2 +2u

8x +y +2 +u

-3x +4y -2z +3u

4x +5y +3z -4u

-9x –y +z +2u

0 +1y +3z +2u

108. 5ab -3bc +4cd, 2bc +2cd -3de, 4bc -2ab +3de, -bc -6cd –ab

5ab -3bc +4cd

       2bc   +2cd -3de

-2ab  4bc         +3de

-ab -3bc -6cd

++2ab       0      0        0

109. 7ª -4b +5c, -7ª +4b -6c

7a -4b +5c

-7a +4b -6c

0     0     -1c

110. 9x -3y +5, -x –y +4, -5x +4y -9

9x -3y +5

-x   –y   +4

-5x +4y -9

+3x 0 0

P +q +r, -2p -6q +3r, p +5q -8r

P +q +r

-2p -6q +3r

P +5q -8r

0     0  -4r   

111. -2m +3n -6, 3m -8n +8, -5m +n -10

-2m +3n -6

3m -8n +8

-5m +n -10

-4m -4n -8

112. ab +bc +cd, -8ab -3bc -3cd, 5ab +2bc +2cd

ab +bc +cd

-8ab -3bc -3cd

5ab +2bc +2cd

-2ab 0 0

113. 5x -7y +8, -y +6 -4x, 9 -3x +8y

5x -7y +8

-4x –y +6

-3x +8y 9

-2x 0 +5

114. 2a +3b, 5c -4, 8a +6, 7c -9

2ª +3b

     6b -4c

-a        +8c

-1ª +3b +4c

115. 8a +3b –c, 5a –b +c, -a –b –c, 7a –b +4c

8a +3b –c

5a –b +c

-a –b –c

7a –b +4c

+19a 0 +3c

116. –m –n –p, m +2n -5, 3p -6m +4, 2n +5m -8

-m –n –p

M +2n    -5

-6m    -3p +4

+5m 2n     -8

-1m +3n +2p -9

117. a +b –c +d, a –b +c –d, -a2 +3b -2c +d, -3a -3b +4c –d

a +b –c +d

a b +c –d

a2 +3b -2c +d

-3a -3b +4c –d

0 0 +2c 0