F.2Maths!!!!!!!!!!!40p!!!!!!

1) 1 - 2a² + a^4
= 1² - 2(1)(a²) + (a²)²
= (1 - a²)²
= (1² - a²)²
= [(1+a)(1-a)]²
= (1+a)²(1-a)²

2) x² - 14x - 72
= (x+4)(x-18)

3) 4x² - 4x - 15
= 4x² - 4x + 1 - 16
= (2x - 1)² - 4²
= (2x-1+4)(2x-1-4)
= (2x+3)(2x-5)

4) 3x² - 7x - 6
= (3x+2)(x-3)

5) 2x² - 22x + 48
= (2x-6)(x-8)

6) 6x³ - 48y³
= 6(x³ - 8y³)
= 6[x³ - (2y)³]
= 6(x - 2y)(x² + 2xy + 4y²)

7) 54y³ + 2x³z^6
= 2(27y³ + x³z^6)
= 2(3y + xz²)(9y² - 3xyz² + x²z^4)

8a) x^4 - 6x² + 9
= (x²)² - 2(x²)(3) + 3²
= (x² - 3)²

b) x^4 - 6x² + 9 - 4x²
= (x² - 3)² - (2x)²
= (x² + 2x - 3)(x² - 2x - 3)
= (x-1)(x+3)(x+1)(x-3)

2009-09-04 23:21:10 補充：
^ = to the power

1)1-2a^2+a^4
=(a^2-1)(a^2-1)
=(a^2-1)^2


2)x^2-14x-72
=(x-18)(x+4)


3)4x^2-4x-15
=(2x+3)(2x-5)


4)3x^2-7x-6
=(3x+2)(x-3)


5)2x^2-22x+48
=2(x^2-11x+24)
=2(x-8)(x-3)

6)6x^3-48y^3
=6[x^3-(2y)^3]
=6(x-2y)(x^2+2xy+4y^2)


7)54y^3+2x^3z^6
=2(27y^3+x^3z^6)
=2[(3y)^3+(xz^2)^3]
=2(3y+xz^2)(9y^2=3xyz^2+x^2Z^4)


8a)Factorize x^4-6x^2+9
x^4-6x^2+9
=(x^2-3)(x^2-3)
=(x^2-3)^2


b)Hence,factorize x^4-6x^2+9-4x^2
x^4-6x^2+9-4x^2
=(x^2-3)^2-4x^2 ----------->x^4-6x^2+9=(x^2-3)^2(from the upper part)
=(x^2-3+4x)(x^2-3-4x) ------------>a^2-b^2=(a+b)(a-b)

1)1－2a^2+a^4
=(1－a^2)^2
=(1－a)^2(1+a)^2

2)x^2－14x－72
=(x^2－18)(x^2+4)

3)4x^2－4x－15
=(2x－5)(2x+3)

4)3x^2－7x－6
=(3x+2)(x－3)

5)2x^2－22x+48
=2(x^2－11x+24)

6)6x^3－48y^3
=6(x^3－8y^3)
=6(x－2y)(x^2+2xy+4y^2)

7)54y^3+2x^3z^6
=2(27y^3+x^3z^6)
=2(3y+xz^2)(9y^2+xz^2+x^2z^4)

8a)Factorize x^4－6x^2+9
=(x^2－3)^2

b)Hence,factorize x^4－6x^2+9－4x^2
=(x^2－3)^2－(2x)^2
=(x^2－2x－3)(x^2+2x－3)
=(x－3)(x+1)(x－1)(x+3)

wt mean by ^?