F.2Maths!!!!!!!!!!!40p!!!!!!
2017/06/29 05:32
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F.2Maths!!!!!!!!!!!40p!!!!!!
發問:
1)1-2a^2+a^4 2)x^2-14x-72 3)4x^2-4x-15 4)3x^2-7x-6 5)2x^2-22x+48 6)6x^3-48y^3 7)54y^3+2x^3z^6 8a)Factorize x^4-6x^2+9 b)Hence,factorize x^4-6x^2+9-4x^2 10)
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
其他解答:
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 ^?
F.2Maths!!!!!!!!!!!40p!!!!!!
發問:
1)1-2a^2+a^4 2)x^2-14x-72 3)4x^2-4x-15 4)3x^2-7x-6 5)2x^2-22x+48 6)6x^3-48y^3 7)54y^3+2x^3z^6 8a)Factorize x^4-6x^2+9 b)Hence,factorize x^4-6x^2+9-4x^2 10)
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最佳解答: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
其他解答:
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 ^?
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