中二數學-因式分解－elahism的部落格

標題:

中二數學-因式分解

發問:

因式分解 1.2(3a-4b)^2-(4b-3a) 2.ax+ay-az+bx+by-bz 3.p^2+qr-q^2-pr 4.(x+1)^2-(y-1)^2 5.8m^2-24mn+18n^2 6.1-2a^2+a^4 8.x^2-14x-72 9.4x^2-4x-15 10.3x^2-7x-6 11.2x^2-22x+48 12.6x^3-48y^3 13.54y^3+2x^3z^6 14.x^4-6x^2+9 15.x^4-6x^2+9-4x^2 16.x^6-1 17.x^4+x^2+1 18.(x+1)^4+(x+1)^2+1

最佳解答:

1.2(3a-4b)^2-(4b-3a) = -2(4b-3a)^2-(4b-3a) = (4b-3a){-2(4b-3a)-1} = (4b-3a)(-8b+6a-1) 2.ax+ay-az+bx+by-bz =x(a+b)+y(a+b)-z(a+b) =(x+y-z)(a+b) 3.p^2+qr-q^2-pr = p^2-pr-q^2+qr = p(p-r)+q(r-q) 4.(x+1)^2-(y-1)^2, a^2-b^2=(a+b)(a-b) = (x+1+y-1)(x+1-y+1) = (x+y)(x-y+2) 5.8m^2-24mn+18n^2 =2{(2m)^2-2(2)(3)(mn)+(3n)^2}, (a-b)^2= a^2-2ab+b^2 =2(2m-3n)^2 6.1-2a^2+a^4 = a^4-2a^2+1 = (a^2)^2-2(a^2)(1)+1^2 = (a^2-1)^2 8.x^2-14x-72 = (x-18)(x+4) 9.4x^2-4x-15 = ( 2x-5)(2x+3) 10.3x^2-7x-6 = (x-3)(3x+2) 11.2x^2-22x+48 = 2(x^2-11x+24) = 2(x-8)(x-3) 12.6x^3-48y^3 = 6(x^3-8y^3), a^3-b^3=(a+b)(a^2-ab+b^2) = 6{x^3-(2y)^3} = 6(x+2y)(x^2-2xy+4y^2) 13.54y^3+2x^3z^6 = 2{ (3y)^3+ (xz^3)^3 } = 2{ (3y)^3+(xz^3)^3 }, a^3+b^3= (a-b)(a^2+ab+b^2) = 2( 3y-xz^3)(9y^2+3xyz^3+x^2z^6) 14.x^4-6x^2+9 = (x^2)^2 -2(x^2)(3) +(3)^2 = (x^2-3)^2 15.x^4-6x^2+9-4x^2 = x^4-10x^2+9 = (x^2)^2-2(x^2)(3)+(3)^2,,你係咪抄錯題目呢,,,, 16.x^6-1 = (x^2)^3-(1)^3 = (x^2+1)(x^4-x^2+1) 17.x^4+x^2+1,18.(x+1)^4+(x+1)^2+1 你係咪抄錯題目呢,,,,

其他解答:

1.2(3a-4b)^2-(4b-3a) = -2(4b-3a)^2-(4b-3a) = (4b-3a){-2(4b-3a)-1} = (4b-3a)(-8b+6a-1) 2.ax+ay-az+bx+by-bz =x(a+b)+y(a+b)-z(a+b) =(x+y-z)(a+b) 3.p^2+qr-q^2-pr = p^2-pr-q^2+qr = p(p-r)+q(r-q) 4.(x+1)^2-(y-1)^2, a^2-b^2=(a+b)(a-b) = (x+1+y-1)(x+1-y+1) = (x+y)(x-y+2) 5.8m^2-24mn+18n^2 =2{(2m)^2-2(2)(3)(mn)+(3n)^2}, (a-b)^2= a^2-2ab+b^2 =2(2m-3n)^2 6.1-2a^2+a^4 = a^4-2a^2+1 = (a^2)^2-2(a^2)(1)+1^2 = (a^2-1)^2 8.x^2-14x-72 = (x-18)(x+4) 9.4x^2-4x-15 = ( 2x-5)(2x+3) 10.3x^2-7x-6 = (x-3)(3x+2) 11.2x^2-22x+48 = 2(x^2-11x+24) = 2(x-8)(x-3) 12.6x^3-48y^3 = 6(x^3-8y^3), a^3-b^3=(a+b)(a^2-ab+b^2) = 6{x^3-(2y)^3} = 6(x+2y)(x^2-2xy+4y^2) 13.54y^3+2x^3z^6 = 2{ (3y)^3+ (xz^3)^3 } = 2{ (3y)^3+(xz^3)^3 }, a^3+b^3= (a-b)(a^2+ab+b^2) = 2( 3y-xz^3)(9y^2+3xyz^3+x^2z^6) 14.x^4-6x^2+9 = (x^2)^2 -2(x^2)(3) +(3)^2 = (x^2-3)^2 15.x^4-6x^2+9-4x^2 = x^4-10x^2+9 = (x^2)^2-2(x^2)(3)+(3)^2 16.x^6-1 = (x^2)^3-(1)^3 = (x^2+1)(x^4-x^2+1) 17.18有問題