因式分解题,急求解!
分解因式:①(m²-1)(n²-1)+4mn②(x²+3x+2)(4x²+8x+3)-90③(x²+xy+y²...
分解因式:①(m²-1)(n²-1)+4mn
②(x²+3x+2)(4x²+8x+3)-90
③(x²+xy+y²)²-4xy(x²+y²)
④(x^5+x^4+x^3+x^2+x+1)²+x^5
⑤(2x²-3x+1)²-22x²+33x-1
⑥(x+y)^3+2xy(1-x-y)-1
⑦(x+3)(x²-1)(x+5)-20
能答多少就写出来多少,我需要的是速度!!! 展开
②(x²+3x+2)(4x²+8x+3)-90
③(x²+xy+y²)²-4xy(x²+y²)
④(x^5+x^4+x^3+x^2+x+1)²+x^5
⑤(2x²-3x+1)²-22x²+33x-1
⑥(x+y)^3+2xy(1-x-y)-1
⑦(x+3)(x²-1)(x+5)-20
能答多少就写出来多少,我需要的是速度!!! 展开
3个回答
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分解因式:①(m²-1)(n²-1)+4mn
=m²n²-m²-n²+1+4mn
=m²n²+2mn+1-m²-n²+2mn
=(mn+1)²-(m²-2mn+n²)
=(mn+1)²-(m-n)²
=(mn+1+m-n)(mn+1-m+n)
②(x²+3x+2)(4x²+8x+3)-90
=(x+2)(x+1)(2x+1)(2x+3)-90
=(x+2)(2x+1)(x+1)(2x+3)-90
=(2x^2+5x+2)(2x^2+5x+3)-90
=(2x^2+5x)^2+5(2x^2+5x)+6-90
=(2x^2+5x)^2+5(2x^2+5x)-84
=(2x^2+5x-7)(2x^2+5x+12)
=(2x+7)(x-1)(2x^2+5x+12)
③(x²+xy+y²)²-4xy(x²+y²)
=(x²+y²)²+2xy(x²+y²)+x²y²-4xy(x²+y²)
=(x²+y²)²-2xy(x²+y²)+x²y²
=(x²+y²-xy)²
④(x^5+x^4+x^3+x^2+x+1)²+x^5
题目应是(x^5+x^4+x^3+x^2+x+1)^2-x^5
=(x^6-1)^2/(x-1)^2-x^5
=[x^12-2x^6+1-x^7+2x^6-x^5]/(x-1)^2
=[(x^7-1)(x^5-1)]/(x-1)^2
=(x^6+x^5+x^4+x^3+x^2+x+1)(x^4+x^3+x^2+x+1)
⑤(2x²-3x+1)²-22x²+33x-1
=(2x²-3x)²+2(2x²-3x)+1-11(2x²-3x)-1
=(2x²-3x)²-9(2x²-3x)
=(2x²-3x)(2x²-3x-9)
=x(2x-3)(2x+3)(x-3)
⑥(x+y)^3+2xy(1-x-y)-1
=(x+y-1)((x+y)^2+(x+y)+1)+2xy(1-x-y)
=(x+y-1)(x^2+y^2+x+y+1)
⑦(x+3)(x²-1)(x+5)-20
=(x+3)(x-1)(x+1)(x+5)-20
=[(x-1)(x+5)][(x+1)(x+3)]-20
=[(x²+4x)-5][(x²+4x)+3]-20
=(x²+4x)²-2(x²+4x)-15-20
=(x²+4x)²-2(x²+4x)-35
=(x²+4x-7)(x²+4x+5)
=m²n²-m²-n²+1+4mn
=m²n²+2mn+1-m²-n²+2mn
=(mn+1)²-(m²-2mn+n²)
=(mn+1)²-(m-n)²
=(mn+1+m-n)(mn+1-m+n)
②(x²+3x+2)(4x²+8x+3)-90
=(x+2)(x+1)(2x+1)(2x+3)-90
=(x+2)(2x+1)(x+1)(2x+3)-90
=(2x^2+5x+2)(2x^2+5x+3)-90
=(2x^2+5x)^2+5(2x^2+5x)+6-90
=(2x^2+5x)^2+5(2x^2+5x)-84
=(2x^2+5x-7)(2x^2+5x+12)
=(2x+7)(x-1)(2x^2+5x+12)
③(x²+xy+y²)²-4xy(x²+y²)
=(x²+y²)²+2xy(x²+y²)+x²y²-4xy(x²+y²)
=(x²+y²)²-2xy(x²+y²)+x²y²
=(x²+y²-xy)²
④(x^5+x^4+x^3+x^2+x+1)²+x^5
题目应是(x^5+x^4+x^3+x^2+x+1)^2-x^5
=(x^6-1)^2/(x-1)^2-x^5
=[x^12-2x^6+1-x^7+2x^6-x^5]/(x-1)^2
=[(x^7-1)(x^5-1)]/(x-1)^2
=(x^6+x^5+x^4+x^3+x^2+x+1)(x^4+x^3+x^2+x+1)
⑤(2x²-3x+1)²-22x²+33x-1
=(2x²-3x)²+2(2x²-3x)+1-11(2x²-3x)-1
=(2x²-3x)²-9(2x²-3x)
=(2x²-3x)(2x²-3x-9)
=x(2x-3)(2x+3)(x-3)
⑥(x+y)^3+2xy(1-x-y)-1
=(x+y-1)((x+y)^2+(x+y)+1)+2xy(1-x-y)
=(x+y-1)(x^2+y^2+x+y+1)
⑦(x+3)(x²-1)(x+5)-20
=(x+3)(x-1)(x+1)(x+5)-20
=[(x-1)(x+5)][(x+1)(x+3)]-20
=[(x²+4x)-5][(x²+4x)+3]-20
=(x²+4x)²-2(x²+4x)-15-20
=(x²+4x)²-2(x²+4x)-35
=(x²+4x-7)(x²+4x+5)
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①(m²-1)(n²-1)+4mn
=m²n²-m²-n²+1+4mn
=m²n²+2mn+1-(m²-2mn+n²)
=(mn+1)²-(m-n)²
=(mn+m-n+1)(mn-m+n+1)
②(x²+3x+2)(4x²+8x+3)-90
③(x²+xy+y²)²-4xy(x²+y²)
=[(x²+y²)+xy]²-4xy(x²+y²)
=(x²+y²)²+2xy(x²+y²)+x²y²-4xy(x²+y²)
=(x²+y²)²-2xy(x²+y²)+x²y²
=(x²-xy+y²)²
④(x^5+x^4+x^3+x^2+x+1)²+x^5
⑤(2x²-3x+1)²-22x²+33x-1
⑥(x+y)^3+2xy(1-x-y)-1
⑦(x+3)(x²-1)(x+5)-20
=m²n²-m²-n²+1+4mn
=m²n²+2mn+1-(m²-2mn+n²)
=(mn+1)²-(m-n)²
=(mn+m-n+1)(mn-m+n+1)
②(x²+3x+2)(4x²+8x+3)-90
③(x²+xy+y²)²-4xy(x²+y²)
=[(x²+y²)+xy]²-4xy(x²+y²)
=(x²+y²)²+2xy(x²+y²)+x²y²-4xy(x²+y²)
=(x²+y²)²-2xy(x²+y²)+x²y²
=(x²-xy+y²)²
④(x^5+x^4+x^3+x^2+x+1)²+x^5
⑤(2x²-3x+1)²-22x²+33x-1
⑥(x+y)^3+2xy(1-x-y)-1
⑦(x+3)(x²-1)(x+5)-20
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①(m²-1)(n²-1)+4mn
=(mn)^2-m^2-n^+1+4mn
=(mn)^2+2mn+1-(m^2-2mn+n^2)
=(mn+1)^2-(m-n)^2
=(mn+m-n+1)(mn-m+n+1)
③(x²+xy+y²)²-4xy(x²+y²)
=(x^2+y^2)^2+2xy(x^2+y^2)+(xy)^2-4xy(x^2+y^2)
=(x^2+y^2)-2xy(x^2+y^2)+(xy)^2
=(x^2+y^2-xy)^2
⑤(2x²-3x+1)²-22x²+33x-1
=(2x^2-3x+1)-11*(2x^2-3x+1)+10
=[(2x^2-3x+1)-1][(2x^2-3x+1)-10]
=x(2x-3)(2x+3)(x-3)
⑥(x+y)^3+2xy(1-x-y)-1
=(x+y)^3-1-2xy(x+y-1)
=[(x+y)-1][(x+y)^2+(x+y)+1]-2xy(x+y-1)
=(x+y-1)(x^2+x+y^2+y+1)
=(mn)^2-m^2-n^+1+4mn
=(mn)^2+2mn+1-(m^2-2mn+n^2)
=(mn+1)^2-(m-n)^2
=(mn+m-n+1)(mn-m+n+1)
③(x²+xy+y²)²-4xy(x²+y²)
=(x^2+y^2)^2+2xy(x^2+y^2)+(xy)^2-4xy(x^2+y^2)
=(x^2+y^2)-2xy(x^2+y^2)+(xy)^2
=(x^2+y^2-xy)^2
⑤(2x²-3x+1)²-22x²+33x-1
=(2x^2-3x+1)-11*(2x^2-3x+1)+10
=[(2x^2-3x+1)-1][(2x^2-3x+1)-10]
=x(2x-3)(2x+3)(x-3)
⑥(x+y)^3+2xy(1-x-y)-1
=(x+y)^3-1-2xy(x+y-1)
=[(x+y)-1][(x+y)^2+(x+y)+1]-2xy(x+y-1)
=(x+y-1)(x^2+x+y^2+y+1)
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