3條f.2數學(續多項式的因式分解)

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1.

12x^2+12x+3
= 3(4x^2+4x+1)
= 3[(4x^2+2x)+(2x+1)]
= 3[2x(2x+1)+1(2x+1)]
= 3[(2x+1)(2x+1)]
= 3(2x+1)^2

2.

45a^2-30a+5
= 5(9a^2-6a+1)
= 5[(9a^2-3a)-(3a-1)]
= 5[3a(3a-1)-1(3a-1)]
= 5[(3a-1)(3a-1)]
= 5(3a-1)^2

3.

18x^2+24x+8
= 2(9x^2+12x+4)
= 2[(9x^2+6x)+(6x+4)]
= 2[3x(3x+2)+2(3x+2)]
= 2[(3x+2)(3x+2)]
= 3(3x+2)^2

2011-08-25 15:04:27 補充：
corr.

3.

18x^2+24x+8
= 2(9x^2+12x+4)
= 2[(9x^2+6x)+(6x+4)]
= 2[3x(3x+2)+2(3x+2)]
= 2[(3x+2)(3x+2)]
= 2(3x+2)^2

1. 12x²+12x+3
=3(4x²+4x+1)
=3[(2x)²+2(2x)(1)+1²]
=3(2x+1)²
2. 45a²-30a+5
=5(9a²-6a+1)
=5[(3a)²-2(3a)(1)+1²]
=5(3a-1)²
3. 18x²+24x+8
=2(9x²+12x+4)
=2[(3x)²+2(3x)(2)+2²]
=2(3x+2)²