簡易多項式的因式分解 (急)

a² = a既二次方

1.
6-54u*2
= 6-54u²
=6(1-9u²).......抽公因數
=6[(1)²-(3u)²]........要知道a²-b²=(a-b)(a+b)
=6(1-3u)(1+3u)

2.
50c*2-8d*2
=50c²-8d²
=2(25c²-4d²).......抽公因數
=2[(5c)²-(2d)²]........要知道a²-b²=(a-b)(a+b)
=2(5c-2d)(5c+2d)


3.
28(x+y)*2-7(x-y)*2
=28(x+y)²-7(x-y)²
=28(x²+2xy+y²)-7(x²-2xy+y²)
=7[4(x²+2xy+y²)-(x²-2xy+y²)].......抽公因數
=7(4x²+8xy+4y²-x²+2xy-y²)
=7(3x²+10xy+3y²)
=7(3x+y)(x+3y)

另一方法 :
28(x+y)²-7(x-y)²
=7[4(x+y)²-(x-y)²].......抽公因數
=7{[2(x+y)]²-(x-y)²}........要知道a²-b²=(a-b)(a+b)
=7(2x+2y+x-y)(2x+2y-x+y)
=7(3x+y)(x+3y)

4.
a*2-b*2+bc-ac
=a²-b²+bc-ac
=(a+b)(a-b)+c(b-a)
=(a+b)(a-b)-c(a-b)........因為(b-a)=-(a-b)
=(a-b)(a+b-c)

5.
4c*2-9d*2-2c-3d
=4c²-9d²-2c-3d
=(2c-3d)(2c+3d)-(2c+3d).........-2c-3d=-(2c+3d)
=(2c+3d)(2c-3d-1)

上述各題, 全部都用到 A*2 - B*2 = (A+B)(A-B)
1. 6 - 54u*2=6(1-9u*2)=6(1*2 - (3u)*2)=6(1+3u)(1-3u)
2. 50c*2-8d*2 = 2(25c*2 - 4d*2) = 2((5c)*2 - (2d)*2)=2(5c+2d)(5c-2d)
3. 28(x+y)*2-7(x-y)*2 = 7(4(x+y)*2 - (x-y)*2)=7((2x+2y)*2 - (x-y)*2) = 7(3x+y)(x+3y)
其他兩題亦類似. 功課應該自己做. 那兩題就自己做吧.