標題:
數學 因式分解
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最佳解答:
因式分解 1. mx－ny+nx－my =mx+nx－ny－my =x(m+n)－y(m+n) =(x－y)(m+n) 2. 18x^2－2y^2+6x－2y =2(9x^2－y^2)+2(3x－y) =2(3x－y)(3x+y)+2(3x－y) =2(3x+y+1)(3x－y) 3. x^2－5x－6 =x^2+x－6x－6 =x(x+1)－6(x+1) =(x－6)(x+1) 4. x^2－4x+4 =(x－2)^2 5. 2x^2－3x－54 =2x^2+9x－12x－54 =x(2x+9)－6(2x+9) =(x－6)(2x+9) 6. 1－y^3 =(1－y)(1+y+y^2) 7. 64x^3－8y^3 =8(8x^3－y^3) =8(2x－y)(4x^2+2xy+y^2) 8. 49a ^2－14a+1－4x^2+4x－1 =( 49a ^2－14a+1)－(4x^2+4x+1) =( 7a－1)^2－(2x+1)^2 =( 7a－1－2x－1)( 7a－1+2x+1) =( 7a－2x－2)( 7a +2x) 9. x^4y－10x^3y^2+25x^2y^3 =x^2y(x^2－10xy+25y^2) =x^2y(x－5y)^2 10. axy^4－ax^4y =axy(y^3－x^3) =axy(y－x)(x^2+xy+y^2) 11. (x+y)^3－(x－y)^3 =(x^3+3x^2y+3xy^2+y^3)－(x^3－3x^2y+3xy^2－y^3) =6x^2y+2y^3 =2y(3x^2+y^2) 12. (x+1)^3－x^3 =(x^3+3x^2+3x+1)-x^3 =3x^2+3x+1
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數學 因式分解
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1. mx-ny+nx-my 2. 18x^2-2y^2+6x-2y 3. x^2-5x-6 4. x^2-4x+4 5. 2x^2-3x-54 6. 1-y^3 7. 64x^3-8y^3 8. 49a^2-14a+1-4x^2+4x-1 9. x^4y-10x^3y^2+25x^2y^3 10. axy^4-ax^4y 11. (x+y)^3-(x-y)^3 12. (x+1)^3-x^3最佳解答:
因式分解 1. mx－ny+nx－my =mx+nx－ny－my =x(m+n)－y(m+n) =(x－y)(m+n) 2. 18x^2－2y^2+6x－2y =2(9x^2－y^2)+2(3x－y) =2(3x－y)(3x+y)+2(3x－y) =2(3x+y+1)(3x－y) 3. x^2－5x－6 =x^2+x－6x－6 =x(x+1)－6(x+1) =(x－6)(x+1) 4. x^2－4x+4 =(x－2)^2 5. 2x^2－3x－54 =2x^2+9x－12x－54 =x(2x+9)－6(2x+9) =(x－6)(2x+9) 6. 1－y^3 =(1－y)(1+y+y^2) 7. 64x^3－8y^3 =8(8x^3－y^3) =8(2x－y)(4x^2+2xy+y^2) 8. 49a ^2－14a+1－4x^2+4x－1 =( 49a ^2－14a+1)－(4x^2+4x+1) =( 7a－1)^2－(2x+1)^2 =( 7a－1－2x－1)( 7a－1+2x+1) =( 7a－2x－2)( 7a +2x) 9. x^4y－10x^3y^2+25x^2y^3 =x^2y(x^2－10xy+25y^2) =x^2y(x－5y)^2 10. axy^4－ax^4y =axy(y^3－x^3) =axy(y－x)(x^2+xy+y^2) 11. (x+y)^3－(x－y)^3 =(x^3+3x^2y+3xy^2+y^3)－(x^3－3x^2y+3xy^2－y^3) =6x^2y+2y^3 =2y(3x^2+y^2) 12. (x+1)^3－x^3 =(x^3+3x^2+3x+1)-x^3 =3x^2+3x+1
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