Factorize

Question 1:     6xy-4xz

Answer:

   6xy-4xz=2x(3y-2z)    

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Question 2:     9bx^2+15b^2 x

Answer:

   9bx^2+15b^2 x=3b x(3x+5b)    

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Question 3:     4a^2 b-6ab^2+8ab

Answer:

   4a^2 b-6ab^2+8ab=2ab (2a-3b+4)     

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Question 4:     5x^2+15x^3-20x

Answer:

   5x^2+15x^3-20x=5x(x+3 x^2-4)     

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Question 5:     2x^3+x^2-4x

Answer:

   2x^3+x^2-4x=x(2x^2+x-4)     

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Question 6:     a^3 b-a^2 b^2-b^3

Answer:

   a^3 b-a^2 b^2-b^3=b (a^3-a^2  b-b^2)     

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Question 7:     28a^2 b^2 c-42ab^2 c^2

Answer:

   28a^2 b^2 c-42ab^2 c^2=14 ab^2 c (2a-3c)    

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Question 8:     15 x^2 y-6xy^2+9y^3

Answer:

   15 x^2 y-6xy^2+9y^3=3y (5x^2-2xy+3y^2 )     

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Question 9:     10x^2 y+15xy^2-25x^2 y^2

Answer:

   10x^2 y+15xy^2-25x^2 y^2=5xy (2x+3y-5xy)    

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Question 10:     18x^2 y-24xyz

Answer:

   18x^2 y-24xyz=6xy (3x-4z)    

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Question 11:     27a^3 b^3-45a^4 b^2

Answer:

   27a^3 b^3-45a^4 b^2=9a^3  b^2  (3b-5a)    

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Question 12:     4(a+b)-6(a+b)^2

Answer:

   4(a+b)-6(a+b)^2=(a+b)(4-6a-6b)     

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Question 13:     2a(3x+5y)-5b(3x+5y) 

Answer:

   2a(3x+5y)-5b(3x+5y)=(3x+5y)(2a-5b)     

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Question 14:     2x(p^2+q^2 )+4y(p^2+q^2 )

Answer:

   2x(p^2+q^2 )+4y(p^2+q^2 )=(p^2+q^2 )(2x+4y)    

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Question 15:     8(3a-2b)^2-10(3a-2b)

Answer:

   8(3a-2b)^2-10(3a-2b)=(3a-2b){8(3a-2b)-10}    

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Question 16:     x(x+y)^3-3x^2 y(x+y)

Answer:

   x(x+y)^3-3x^2 y(x+y)=x(x+y){(x+y)^2-3xy}=x(x+y)(x^2+y^2-2y)    

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Question 17:    a(3x-2y)+b(2y-3x)

Answer:

   a(3x-2y)+b(2y-3x)=(3x-2y)(a-b)     

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Question 18:     a(b-c)^2-d(c-b)

Answer:

   a(b-c)^2-d(c-b)=(b-c){a(b-c)+d}     

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Question 19:     a(4a-b)+2b(4a-b)-c(4a-b)

Answer:

   a(4a-b)+2b(4a-b)-c(4a-b)=(4a-b)(a+2b-c)    

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Question 20:     m(mx+ny)^2+mn(mx+ny)+n(mx+ny)

Answer:

   m(mx+ny)^2+mn(mx+ny)+n(mx+ny)=(mx+ny)(m^2 x+mny+mn+n)