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(1)
15ax+3bx-20ay+4by
=5a(3x-4y)+b(3x+4y)

(2)
4t3次方- 4t2次方 +t -1
=4t^3-4t^2+t-1
=4t^2(t-1)+(t-1)
=(4t^2+1)(t-1)

(3)
2a２次方-6a２y -21by+7bx
=2a^2-6a^2y -21by+7bx
=2a^2(1-3y)-7b(3y-x)

(4)
36x２次方- 49
=36x^2-7^2
(36x+7)(36x-7)

(5)
4x２次方-25
=4x^2-5^2
=(4x+5)(4x-5)

(6)
16x２次方+8x+1
=16x^2+8x+1
=(4x)^2+2(4x)(1)+1^2
=(4x+1)^2

(7)
4x２次方+4x+1
=4x^2+4x+1
=(2x)^2+2(2x)(1)+1^2
=(2x+1)^2

(8)
9a３次方-30a２次方b+25ab２次方
=9a^3-30a^2b+25ab^2
=a(9a^2-30ab+25b^2)
=a<(3a)^2-2(3a)(5b)+(5b)^2>
=a(3a-5b)^2

1)
15ax+3bx-20ay+4by
=5a(3x-4y)+b(3x+4y)

2)
4t3次方- 4t2次方 +t -1
=4t^3-4t^2+t-1
=4t^2(t-1)+(t-1)
=(4t^2+1)(t-1)

3)
2a２次方-6a２y -21by+7bx
=2a^2-6a^2y -21by+7bx
=2a^2(1-3y)-7b(3y-x)

4)
36x２次方- 49
=36x^2-7^2
(36x+7)(36x-7)

5)
4x２次方-25
=4x^2-5^2
=(4x+5)(4x-5)

6)
16x２次方+8x+1
=16x^2+8x+1
=(4x)^2+2(4x)(1)+1^2
=(4x+1)^2

7)
4x２次方+4x+1
=4x^2+4x+1
=(2x)^2+2(2x)(1)+1^2
=(2x+1)^2

8)
9a３次方-30a２次方b+25ab２次方
=9a^3-30a^2b+25ab^2
=a(9a^2-30ab+25b^2)
=a<(3a)^2-2(3a)(5b)+(5b)^2>
=a(3a-5b)^2