URGENT!!! F.2 Maths

Factorize the following

1.(m+n)^2-6(m+n)+9
=(m+n)^2-(2)(3)(m+n)+3^2
=(m+n-3)^2

2. 9(2p+3)^2+12(2p+3)+4
=[(3)(2p+3)]^2 + (2)(3)(2p+3)(2) + 2^2
=[(3)(2p+3)+2]^2

3.3-6b+3b^2
=3(b^2-2b+1)
=3(b-1)^2

4. 2ax^2-8axy+8ay^2
=2a ( x^2 - 4xy + 4y^2)
=2a ( x^2 - (2)(2)xy + (2y)^2 )
=2a ( x -2y )^2

5. 4-4(p-q)+(p-q)^2
=(p-q)^2 - (2)(2)(p-q) + 2^2
=(p-q-2)^2

6* 2(x-3)^2-4(x-3)+2
=2[ (x-3)^2 - 2(x-3) + 1]
=2 [ (x-3-1)^2]
=2(x-4)^2

7 12x^2-38x-72
=2 (6x^2 - 19x - 36)
=2 (-9+2 x) (4+3 x)

8 3x^3-7x^2+2x
=x (3x^2 - 7x + 2)
=x (-2+x) (-1+3 x)

9 2x^3-5x^2+2x
=x (2x^2 - 5x + 2)
=x (-2+x) (-1+2 x)

10 2x^3-x^2-6x+3
=(-1+2 x) (-3+x^2)

11.(x^2-2x-1)^2-4
=(x^2-2x-1)^2 - 2^2
=(x^2-2x-1+2)(x^2-2x-1-2)
=(x^2-2x+1)(x^2-2x-3)

12. 2x^5-32x
=2x^5 - (2^5)x
=2x (x^4 - 2^4)
=2x ( (x^2)^2 - (2^2) ^2)
=2x ( x^2 - 2^2 ) ( x^2 + 2^2)
=2x (x-2)(x+2)(x^2+2^2)

13.Which of the following has a factor of (2x+y)

A. 2x^2+y^2
B.4x^2+y^2
C.2x^2+2xy+y^2
D.4x^2+4xy+y^2 = (2x+y)^2

Thus the answer is D

14. ( 2x^2-2)/(2x^2+x-1)
= [2(x-1)(x+1)] / [(x+1)(2x-1)]
= [2(x-1)] / (2x-1)

15.(px+p/x-1)/[(2px+2p)/(x^2-1)]

可唔可以打清楚啲? 唔太明條題目

2012-10-23 16:21:58 補充：
Q2

=[(3)(2p+3)+2]^2
=(6p+11)^2

2012-10-23 16:23:25 補充：
Part of Q15

[(2px+2p)/(x^2-1)]
=[(2p)(x+1)/(x+1)(x-1)]
=[(2p)/(x-1)]

2012-10-23 21:37:02 補充：
Q15
[px+p/(x-1)] / [(2px+2p)/(x^2-1)]
= {[px(x-1)+p] / (x-1)} / {[2p(x+1)] / [(x+1)(x-1)]}
= {[p(x^2-x+1)] / (x-1)} / [2p / (x-1)]
= {[p(x-1)^2] / (x-1)} / [2p / (x-1)]
= [p(x-1)^2] / (2p)
= [(x-1)^2] / p

1.(m+n)^2-6(m+n)+9
=[(m+n)-3]^2
=(m+n-3)^2

2.9(2p+3)^2+12(2p+3)+4
=[3(2p+3)]^2+2[3(2p+3)](2)+2^2
=[3(2p+3)+2]^2
=(6p+11)^2

3.3-6b+3b^2
=3(1-2b+b^2)
=3(b-1)^2

4. 2ax^2-8axy+8ay^2
=2a(x^2-4xy+4y^2)
=2a(x-2y)^2

5. 4-4(p-q)+(p-q)^2
=2^2-2(2)(p-q)+(p-q)^2
=(p-q-2)^2

6. 2(x-3)^2-4(x-3)+2
=2[(x-3)^2+2(x-3)+1]
=2(x-3+1)^2
=2(x-2)^2

7. 12x^2-38x-72
=2(6x^2-19x-36)
=2(3x+4)(2x-9)

8. 3x^3-7x^2+2x
=x(3x^2-7x+2)
=x(3x-1)(x-2)

9. 2x^3-5x^2+2x
=x(2x^2-5x+2)
=x(2x+1)(x+2)

10. 2x^3-x^2-6x+3
=x^2(2x-1)-2(2x-1)
=(x^2-2)(2x-1)

11.(x^2-2x-1)^2-4
=(x^2-2x-1)^2-2^2
=[(x^2-2x-1)+2][(x^2-2x-1)-2]
=(x^2+2x+1)(x^2+2x-3)
=(x+1)^2(x+3)(x-1)

12. 2x^5-32x
=2x(x^4-16)
=2x[(x^2+4)(x^2-4)]
=2x(x^2+4)(x+2)(x-2)

13.Which of the following has a factor of (2x+y)
A. 2x^2+y^2
B.4x^2+y^2
C.2x^2+2xy+y^2
D.4x^2+4xy+y^2
Ans. D
4x^2+4xy+y^2=(2x+y)^2

14. (2x^2-2)/(2x^2+x-1)
=[2(x^2-1)]/[(2x-1)(x+1)]
=[2(x+1)(x-1)]/[(2x-1)(x+1)]
=[2(x-1)]/(2x-1)
15.[px+p/(x-1)]/[(2px+2p)/(x^2-1)]
={[px(x-1)+p]/(x-1)}/{[2p(x+1)]/[(x+1)(x-1)]}
={[p(x^2-x+1)]/(x-1)}/[2p/(x-1)]
={[p(x-1)^2]/(x-1)}/[2p/(x-1)]
=[p(x-1)^2]/(2p)
=[(x-1)^2]/p

^means...?