F.3數學 help!! T__T

唔好咁講~
最緊要而家學識左佢!
呢d知識肯定你之後考試仲有用~
所以一定要學明白。

1. (4m²+12m+9)-4m-6 = (2m+3)²-2(2m+3) = (2m+3)(2m+3-2) = (2m+3)(2m+1)

2. m²-10m+25-n² = (m-5)² - n² = (m-5+n)(m-5-n) = (m+n-5)(m-n-5)

3. (x²-2x-15)+3ax-15a = (x-5)(x+3)+3a(x-5) = (x-5)(x+3+3a)

4. (x³-3x²)-(3x²-14x+15) = x²(x-3)-(3x-5)(x-3) = (x-3)(x²-3x+5)

5a). m³-8n³ = m³-(2n)³ = (m-2n)(m²+2mn+4n²)

5b) m³-8n³-4m+8n = (m-2n)(m²+2mn+4n²)-4(m-2n) = (m-2n)(m²+2mn+4n²-4) = (m-2n)(m²+2mn+4n²-4)

6a).16m³+2n³ = 2(8m³+n³) = 2[(2m)³+n³] = 2(2m+n)(4m²-2mn+n²)

6b) 16m³+2n³-10m-5n = 2(2m+n)(4m²-2mn+n²)-5(2m+n) = (2m+n)[2(4m²-2mn+n²)-5] = (2m+n)(8m²-4mn+2n²-5)

7a) 27m³+125n³ = (3m)³ + (5n)³ = (3m+5n)(9m²-15mn+25n²)

7b) (27m³+125n³)+9m²-25n² = (3m+5n)(9m²-15mn+25n²)+9m²-25n² = (3m+5n)(9m²-15mn+25n²)+(3m+5n)(3m-5n) = (3m+5n)[(9m²-15mn+25n²)+(3m-5n)] = (3m+5n)(9m²-15mn+25n²+3m-5n)

8. (a+2b)²-(2a-b)² = [(a+2b)+(2a-b)][(a+2b)-(2a-b)] = (a+2b+2a-b)(a+2b-2a+b) = (3a+b)(3b-a)

9. (c+d)³+(c-d)³ = [(c+d)+(c-d)][(c+d)²-(c+d)(c-d)+(c-d)²] = (2c)(c²+2cd+d²-c²+d²+c²-2cd+d²) = (2c)(d²+d²+c²+d²) = 2c(c²+3d²)

10. Make x the subject of the formula.
[請注意: 你應該小心加上括號。]
(1-x)/(1-y) = (2-x)/(2-y)
(1-x)(2-y) = (2-x)(1-y)
2-y-2x+xy = 2-2y-x+xy
-y-2x = -2y-x
2y-y = -x+2x
y=x
x=y

1. (4m²+12m+9)-4m-6
=4m²+8m+3
=(2m+3)(2m+1)

2. m²-10m+25-n²
=(m-5)²-n²
=[(m-5)+n][(m-5)-n]
=(m+n-5)(m-n-5)

3. (x²-2x-15)+3ax-15a
=(x-5)(x+3)+3a(x-5)
=(x+3+3a)(x-5)

4. (x³-3x²)-(3x²-14x+15)
=x²(x-3)-(3x-5)(x-3)
=(x²-3x-5)(x-3)

5a). m³-8n³
=m³-(2n)³
=(m-2n)[m²+2nm+(2n)²]
=(m-2n)(m²+2nm+4n²}

5b) m³-8n³-4m+8n
=(m-2n)(m²+2nm+4n²)-4m+8n
=(m-2n)(m²+2nm+4n²)-4(m-2n)
=(m²+2nm+4n²-4)(m-2n)

6a).16m³+2n³
=2(8m³+n³)
=2[(2m)³+n³]
=2{(2m+n)[(2m)²-2mn+n²]}
=2[(2m+n)(4m²-2mn+n²)]
=(2m+n)(8m²-4mn+2n²)

6b) 16m³+2n³-10m-5n
=(2m+n)(8m²-4mn+2n²)-10m-5n
=(2m+n)(8m²-4mn+2n²)-5(2m+n)
=(8m²-4mn+2n²-5)(2m+n)

7a) 27m³+125n³
=(3m)³+(5n)³
=(3m+5n)[(3m)²-(3m)(5n)+(5n)²]
=(3m+5n)(9m²-15mn+25n)

7b) (27m³+125n³)+9m²-25n²
=(3m+5n)(9m²-15mn+25n)+9m²-25n²
=(3m+5n)(9m²-15mn+25n)+(3m)²-(5n)²
=(3m+5n)(9m²-15mn+25n)+(3m+5n)(3m-5n)
=(3m+5n)(9m²-15mn+25n+3m+5n)
=(3m+5n)(9m²-15mn+30n+3m)

8. (a+2b)²-(2a-b)²
=[(a+2b)+(2a-b)][(a+2b)-(2a-b)]
=(a+2b+2a-b)(a+2b-2a+b)
=(3a+b)(3b-a)

9. (c+d)³+(c-d)³
=[(c+d)+(c-d)][(c+d)²-(c+d)(c-d)+(c-d)²]
=(2c)[c²+2cd+d²-(c²-d²)+c²-2cd+d²]
=(2c)[c²+2cd+d²-c²+d²+c²-2cd+d²]
=(2c)(c²+3d²)

10. Make x the subject of the formula.
1-x/1-y = 2-x/2-y
(1-x)(2-y)=(1-y)(2-x)
2-y-2x+xy=2-x-2y+xy
-y-2x=-x-2y
x-2x=y-2y
x(1-2)=y(1-2)
x=y


做死我了......

2013-08-17 05:38:54 補充：
Masterijk做得好快@@b
自愧不如......

2013-08-17 05:39:24 補充：
當係綀習下=]