因式分解:併項~(40點)~快~!

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問：因式分解

答：

1. 25x^2+15xy

= x(25x+15y)
= 5x(5x+3y)

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2. -25y-5xy-y^2

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

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3. x(x+y)+2(x+y)

= (x+2)(x+y)

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4. 2x+2x^2+y+xy

= 2x(1+x) + y(1+x)
= (2x+y)(1+x)

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5. 2p+ap+2q+aq

= p(2+a) + q(2+a)
= (p+q)(2+a)

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6. ax+b-ax^2-bx

= (ax-ax^2) + (b-bx)
= ax(1-x) + b(1-x)
= (ax+b)(1-x)

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7. x^2+xy+3x+3y

= x(x+y) + 3(x+y)
= (x+3)(x+y)

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8. x^3-2x^2+3x-6

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

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9. 6ax-2bx-10cx+3ay-by-5cy

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

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1. x(25x+15y) = 5x(5x+3y)
2. -(25y+5xy+y^2) = -y(25+5x+y)
3. (x+y)(x+2)
4. 2x(1+x)+y(1+x) = (1+x)(2x+y)
5. p(2+a)+q(2+a) = (2+a)(p+q)
6. ax(1-x)+b(1-x) = (1-x)(ax+b)
7. x(x+3)+y(x+3) = (x+3)(x+y)
8. x(x^2+3)-2(x^2+3) = (x^2+3)(x-2)
9. 2x(3a-b-5c)+y(3a-b-5c)=(3a-b-5c)(2x+y)

1. 25x^2+15xy
=5x(5x+3y)

2. -25y-5xy-y^2
= -y(25+5x+y)

3. x(x+y)+2(x+y)
=(x+y)(x+2)

4. 2x+2x^2+y+xy
=2x(1+x)+y(1+x)
=(1+x)(2x+y)

5. 2p+ap+2q+aq
=p(2+a)+q(2+a)
=(2+a)(p+q)

6. ax+b-ax^2-bx
=ax-ax^2+b-bx
=ax(1-x)+b(1-x)
=(1-x)(ax+b)

7. x^2+xy+3x+3y
=x^2+3x+xy+3y
=x(x+3)+y(x+3)
=(x+3)(x+y)

8. x^3-2x^2+3x-6
=x^2(x-2)+3(x-2)
=(x^2+3)(x-2)

9. 6ax-2bx-10cx+3ay-by-5cy
=2x(3a-b-5c)+y(3a-b-5c)
=(3a-b-5c)(2x+y)