Factorize

Question 1:  5xy+20x-9y-36

Answer:

5xy+20x-9y-36  = 5x(y+4)-9(y+4)  = (y+4)(5x-9)

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Question 2:  5ab-10b-7a+14

Answer:

5ab-10b-7a+14  = 5b(a-2)-7(a-2)  = (a-2)(5b-7)

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Question 3: 9xy+7y-9y^2-7x

Answer:

9xy+7y-9y^2-7x  = 9y(x-y)-7(x-y)  = (x-y)(9y-7)

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Question 4: 3ax-6ay-8by+4bx

Answer:

3ax-6ay-8by+4bx = 3a(x-y)+4b(x-y)= (x-y)(3a+4b)

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Question 5: 4x^2-10xy-6xz+15yz

Answer:

4x^2-10xy-6xz+15yz = 2x(2x-5y)-3z(2x-5y) = (2x-5y)(2x-3z)

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Question 6: 3ab-6bc-3ax+6cx

Answer:

3ab-6bc-3ax+6cx = 3b(a-2c)-3x(a-2c) = (a-2c)(3b-3x)

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Question 7: a^2+ab(1+b)+b^3

Answer:

a^2+ab(1+b)+b^3

= a^2+ab+ab^2+b^3

= a(a+b)+b^2 (a+b)

= (a+b)(a+b^2)

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Question 8: xy^2+(x-1)y-1

Answer:

xy^2+(x-1)y-1

= xy^2+xy-y-1

= xy(y+1)-1(y+1)

= (y+1)(xy-1)

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Question 9: b^2-ab(1-a)-a^3

Answer:

b^2-ab(1-a)-a^3

= b^2-ab+a^2 b-a^3

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

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

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Question 10: y^2-y(2b+a)+2ab

Answer:

y^2-y(2b+a)+2ab

= y^2-2yb-ya+2ab

= y(y-2b)-a(y-2b)

= (y-2b)(y-a)

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Question 11: x-2-(x-2)^2+ax-2a

Answer:

x-2-(x-2)^2+ax-2a

= (x-2)[1-(x-2)]+a(x-2)

= (x-2)(1-x+2-a)

= (x-2)(3-x-a)

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Question 12: x-1-(x-1)^2+4-4x

Answer:

x-1-(x-1)^2+4-4x

= (x-1)(1-(x-1))-4(x-1)

= (x-1)(1-x+1-4)

= (x-1)(-x-2)

= (1-x)(x+2)

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Question 13: b(c-d)^2-a(d-c)+5c-5d

Answer:

b(c-d)^2-a(d-c)+5c-5d

= b(c-d)^2-a(d-c)+5(c-d)

= (c-d)[b(c-d)-a+5]

= (c-d)(bc-bd-a+5)

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Question 14: ab(c^2+b^2 )-a^2 cd-b^2 cd

Answer:

ab(c^2+b^2 )-a^2 cd-b^2 cd

= abc^2+abd^2-a^2 cd-b^2 cd

= ac(bc-ad)+bd(ad-bc)

= (bc-ad)(ac-bd)

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Question 15: ab(x^2+y^2 )+xy(a^2+b^2 )

Answer:

ab(x^2+y^2 )+xy(a^2+b^2 )

= abx^2+aby^2+xya^2+xyb^2

= ax(bx+ay)+by(ay+bx)

= (bx+ay)(ax+by)

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Question 16: ab(x^2+y^2 )-xy(a^2+b^2 )

Answer:

ab(x^2+y^2 )-xy(a^2+b^2 )

= abx^2+aby^2-xya^2-xyb^2

= ax(bx-ay)+by(ay-bx)

= (bx-ay)(ax-by)

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Question 17: (ax+by)^2+(bx-ay)^2

Answer:

(ax+by)^2+(bx-ay)^2

= a^2 x^2+b^2 y^2+2abxy+b^2 x^2+a^2 y^2-2abxy

= a^2 x^2+b^2 y^2+b^2 x^2+a^2 y^2

= a^2 (x^2+y^2 )+b^2 (x^2+y^2 )

= (x^2+y)(a^2+b^2)

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Question 18: a(a+b+c)-bc

Answer:

a(a+b+c)-bc

= a^2+ab-ac-bc

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

= (a-c)(a+b)

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

Answer:

a(a-2b-c)+2bc

= a^2-2ab-ac+2bc

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

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

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Question 20: 3x^5-6x^4-2x^3+4x^2+x-2

Answer:

3x^5-6x^4-2x^3+4x^2+x-2

= 3x^4 (x-2)-2x^2 (x-2)+(x-2)

= (x-2)(3x^4-2x^2+1)

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Question 21: 2a+2b-3cx-3bx+2c-3ax

Answer:

2a+2b-3cx-3bx+2c-3ax 

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

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

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Question 22: a^2 b^2+b^2+a^2+1

Answer:

a^2 b^2+b^2+a^2+1

= b^2 (a^2+1)+(a^2+1) 

= (a^2+)(b^2+1)