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Mathematics
Perform the nnamerome
  1. ( 12 y 2 + 17 y 4 ) ÷ ( 9 y 2 13 y + 3 ) = (12y^(2)+17 y-4)-:(9y^(2)-13 y+3)=
    2 ( 2 x 3 + 7 x 2 + x ) + ( 2 x 2 4 x 12 ) = 2(2x^(3)+7x2+x)+(2x^(2)-4x-12)=
  2. ( 3 m 2 + m ) + ( 4 m 2 + 6 m ) = (-3m^(2)+m)+(4m^(2)+6m)=
  3. ( 7 z 3 + 4 z 1 ) + ( 2 z 2 6 z + 2 ) = (7z^(3)+4z-1)+(2z^(2)-6z+2)=
  4. ( 3 a 2 + 2 a 2 ) ( a 2 3 a + 7 ) = (3a^(2)+2a-2)-(a^(2)-3a+7)=
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  1. ( 12 y 2 + 17 y 4 ) ÷ ( 9 y 2 13 y + 3 ) = 4 3 (12y^(2)+17 y-4)-:(9y^(2)-13 y+3)=(4)/(3)
    Solution:
    We can solve this problem using long division method or synthetic division method. Using synthetic division method, we get:
    Undefined control sequence \cline
    Therefore, ( 12 y 2 + 17 y 4 ) ÷ ( 9 y 2 13 y + 3 ) = 4 3 (12y^(2)+17 y-4)-:(9y^(2)-13 y+3)=(4)/(3)
  2. 2 ( 2 x 3 + 7 x 2 + x ) + ( 2 x 2 4 x 12 ) = 4 x 3 + 18 x 2 5 x 12 2(2x^(3)+7x2+x)+(2x^(2)-4x-12)=4x^(3)+18x^(2)-5x-12
    Solution:
    We can simplify the given expression as follows:
    2 ( 2 x 3 + 7 x 2 + x ) + ( 2 x 2 4 x 12 ) = 4 x 3 + 14 x 2 + 2 x + 2 x 2 4 x 12 2(2x^(3)+7x2+x)+(2x^(2)-4x-12)=4x^(3)+14x^(2)+2x+2x^(2)-4x-12
    = 4 x 3 + 18 x 2 5 x 12 =4x^(3)+18x^(2)-5x-12
    Therefore, 2 ( 2 x 3 + 7 x 2 + x ) + ( 2 x 2 4 x 12 ) = 4 x 3 + 18 x 2 5 x 12 2(2x^(3)+7x2+x)+(2x^(2)-4x-12)=4x^(3)+18x^(2)-5x-12
  3. ( 3 m 2 + m ) + ( 4 m 2 + 6 m ) = m 2 + 7 m (-3m^(2)+m)+(4m^(2)+6m)=m^(2)+7m
    Solution:
    We can simplify the given expression as follows:
    ( 3 m 2 + m ) + ( 4 m 2 + 6 m ) = 3 m 2 + 4 m 2 + m + 6 m (-3m^(2)+m)+(4m^(2)+6m)=-3m^(2)+4m^(2)+m+6m
    = m 2 + 7 m =m^(2)+7m
    Therefore, ( 3 m 2 + m ) + ( 4 m 2 + 6 m ) = m 2 + 7 m (-3m^(2)+m)+(4m^(2)+6m)=m^(2)+7m
  4. ( 7 z 3 + 4 z 1 ) + ( 2 z 2 6 z + 2 ) = 7 z 3 + 2 z 2 2 z + 1 (7z^(3)+4z-1)+(2z^(2)-6z+2)=7z^(3)+2z^(2)-2z+1
    Solution:
    We can simplify the given expression as follows:
    ( 7 z 3 + 4 z 1 ) + ( 2 z 2 6 z + 2 ) = 7 z 3 + 2 z 2 + ( 6 z + 4 z ) 1 + 2 (7z^(3)+4z-1)+(2z^(2)-6z+2)=7z^(3)+2z^(2)+(-6z+4z)-1+2
    = 7 z 3 + 2 z 2 2 z + 1 =7z^(3)+2z^(2)-2z+1
    Therefore, ( 7 z 3 + 4 z 1 ) + ( 2 z 2 6 z + 2 ) = 7 z 3 + 2 z 2 2 z + 1 (7z^(3)+4z-1)+(2z^(2)-6z+2)=7z^(3)+2z^(2)-2z+1
  5. ( 3 a 2 + 2 a 2 ) ( a 2 3 a + 7 ) = 2 a 2 a 9 (3a^(2)+2a-2)-(a^(2)-3a+7)=2a^(2)-a-9
    Solution:
    We can simplify the given expression as follows:
    ( 3 a 2 + 2 a 2 ) ( a 2 3 a + 7 ) = 3 a 2 + 2 a 2 a 2 + 3 a 7 (3a^(2)+2a-2)-(a^(2)-3a+7)=3a^(2)+2a-2-a^(2)+3a-7
    = 2 a 2 a 9 =2a^(2)-a-9
    Therefore, ( 3 a 2 + 2 a 2 ) ( a 2 3 a + 7 ) = 2 a 2 a 9 (3a^(2)+2a-2)-(a^(2)-3a+7)=2a^(2)-a-9
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