[15分] Maths Questions (Polynomials) 要列明步驟 =]

1) (x+1)(x+4)
=(x+1)x+(x+1)4
=(x^2+x)+(4x+4)
=x^2+5x+4

2)(2x-1)(x+5)
=(2x-1)x+(2x-1)5
=(2x^2-x)+(10x-5)
=2x^2+9x-5

3. (3n+2)^2
=(3n)^2+2(3n)(2)+(2)^2 (identities:(a+b)^2 = a^2+2ab+b^2 )
=9n^2+12n+4

4. (2n-10)^2
=(2n)^2-2(2n)(10)+(10)^2 (identities:(a-b)^2 = a^2-2ab+b^2 )
=4n^2-40n+100

5. (k-3)(k+3)
=k^2 - 3^2 (identities:(a-b)(a+b) = a^2-b^2 )
=k^2 - 9

6. (3-4y)(4y+3)
= -(4y-3)(4y+3) ( (a-b) = -(b-a) ，方便計)
=(4y)^2 - (3)^2
=16y^2 - 9

7. 3(a+b) + (c-4) (a+b)
=(a+b)(3+c-4) (抽個comon factor出尼)
=(a+b)(c-1)

8. 6ch - dh - 6ck + dk
=6c(h-k)-d(h-k)
=(6c-d)(h-k)

9. 3x^2 + 2xy - 3x - 2y
=3x(x-1)+2y(x-1)
=(3x+2y)(x-1)

(x+1)(x+4)
=x^2+4x+x+4
=x^2+5x+4

2. (2x-1)(x+5)
=2x^2+10x-x-5
=2x^2+9x-5

3. (3n+2)^2
=(3n+2)(3n+2)
=9n^2+6n+6n+4
=9n^2+12n+4

4. (2n-10)^2
=(2n-10)(2n-10)
=4n^2-20n-20n+100
=4n^2-40n+100

5. (k-3)(k+3)
=k^2+3k-3k-9
=k^2-9

6. (3-4y)(4y+3)
=12y+9-16y^2-12y
=9-16y^2

7. 3(a+b) + (c-4) (a+b)
=3a+3b+(ca+cb-4a-4b)
=3a+3b+ca+cb-4a-4b
= ca+cb-a-b
=a(c-1)+b(c-1)
=(a+b)(c-1)

8. 6ch - dh - 6ck + dk
=h(6c-d)-k(6c-d)
=(6c-d)(h-k)

9. 3x^2+ 2xy - 3x - 2y
=3x(x-1)+2y(x-1)
=(3x+2y)(x-1)

2007-08-14 13:13:06 補充：
http://218.191.100.122/discuz/viewthread.php?tid=35&extra=page%3D1

1. (x+1)(x+4)
=x^2+4x+x+4
=x^2+5x+4

2. (2x-1)(x+5)
=2x^2+10x-x-5
=2x^2+9x-5

3. (3n+2)^2
=(3n+2)(3n+2)
=9n^2+6n+6n+4
=9n^2+12n+4

4. (2n-10)^2
=(2n-10)(2n-10)
=4n^2-20n-20n+100
=4n^2-40n+100

5. (k-3)(k+3)
=k^2+3k-3k-9
=k^2-9

6. (3-4y)(4y+3)
=12y+9-16y^2-12y
=-16y^2+12y-12y+9
=-16y^2+9

7. 3(a+b) + (c-4) (a+b)
=3a+3b+(ac+bc-4a-4b)
=3a-4a+3b-4b+ac+bc
=-a-b+ac+bc

8. 6ch - dh - 6ck + dk(can't simplify or expand)

9. 3x^2 + 2xy - 3x - 2y(can't simplify or expand)

1. (x+1)(x+4)=x^2+4x+x+4=x^2+5x+4

2. (2x-1)(x+5)=2x^2+10x-x-5=2x^2+9x-5

3. (3n+2)^2=(3n)^2+2*3n*2+2^2=9n^2+12n+4

4. (2n-10)^2=(2n)^2-2n*10*2+10^2=4n^2-40n+100

5. (k-3)(k+3)=k^2-9

6. (3-4y)(4y+3)=(3-4y)(3+4y)=9-16y^2

7. 3(a+b) + (c-4) (a+b)=(a+b)(3+c-4)=(a+b)(c-1)

8. 6ch - dh - 6ck + dk=(6ch-dh)-(6ck-dk)=h(6c-d)-k(6c-d)=(6c-d)(h-k)

9. 3x^2 + 2xy - 3x - 2y=(3x^2-3x)+(2xy-2y)=3x(x-1)+2y(x-1)=(x-1)(3x+2y)