F. 2 maths (Factorize)

1. x^2-(x+y)^2
=[x+(x+y)][x-(x+y)]
= -(2x+y)y

2. (4x - 5y)^2 - (5x - 4y)^2
=[4x-5y+(5x-4y)][4x-5y-(5x-4y)]
=(9x-9y)(-x-y)
=-9(x-y)(x+y)

3. 4(2x + y)^2 - (x + 2y)^2
= [2(2x+y)]^2 - (x+2y)^2
= [2(2x+y) + (x+2y)][2(2x+y) - (x+2y)]
= (4x+2y+x+2y)(4x+2y-x-2y)
= 3x(5x+4y)

4. 12 - 3(e + 2f)^2
= 3[4-(3e+2f)^2]
= 3[2^2 - (3e+2f)^2]
= 3[2+(3e+2f)][2-(3e+2f)]
= 3(2+3e+2f)(2-3e-2f)

5. 98(g - h)^2 - 50g^2
= 2[49(g-h)^2 - 25g^2]
= 2{ [7(g-h)]^2 - (5g)^2 }
= 2[7(g-h)+5g][7(g-h)-5g]
= 2(7g-7h+5g)(7g-7h-5g)
= 2(12g-7h)(2g-7h)

6. 75k - 3k(2k - 1)^2
= 3k[25 - (2k-1)^2]
= 3k[5^2 - (2k-1)^2]
= 3k[5+(2k-1)][5-(2k-1)]
= 3k(4+2k)(6-2k)
= 3k(2)(2)(2+k)(3-k)
= 12k(2+k)(3-k)

7. 8q^2 + 2r + 4q - 2r^2
= 8q^2-2r^2+2r+4q
= 2(4q^2-r^2) + 2(r+2q)
= 2(2q+r)(2q-r) + 2(r+2q)
= (2q+r)[2(2q-r)+2]
= (2q+r)(4q-2r+2)

8. -2q^4 + 2q^3 + 2q^2 - 1
= -2q^2(q^2-q-1) -1
i.e. Check whether the question is right or wrong because all the questions are about a^2-b^2=(a+b)(a-b)

9. 1+36c^2 d^2 - 4c^2 - 9d^2
= 1 - 4c^2 + 36c^2 d^2 - 9d^2
= (1+2c)(1-2c) + (6cd+3d)(6cd-3d)
= (1+2c)(1-2c) + (3d)(3d)(2c+1)(2c-1)
= (1+2c)(1-2c) - (3d)(3d)(1+2c)(1-2c)
= (1+2c)(1-2c)[1-(3d)(3d)]
= (1+2c)(1-2c)(1-9d^2)
= (1+2c)(1-2c)(1+3d)(1-3d)








2009-10-19 19:27:20 補充：
Please check if the answer is correct or wrong.
Remind me so that I can correct it~