( Bài 6: Phân tích thành nhân tử ( phối hợp các phương pháp )
5) 4x^5y^2 + 8x^4y^3 + 4x^3y^4 ;
9) 4x^5y^2 + 16x^4y^2 + -6x^3y^2 ;
13) -3x^4y + 6x^3y -3x^2y ;
17) 8x^3 - 8x^2y + 2xy^2 ;
21) (a^2 + 4) ^2 - 16a^2b^2 ;
25) 100a^2 - (a^2 + 25)^2 ;
29) 25a^2b^2 - 4x^2 + 4x - 1 ;
33) 1 - 2m + m^2 - x^2 - 4x - 4 ;
37) ax^2 + bx^2 + 2xy(a + b) + 2ay^2 + by^2 ;
41) 5a^2 - 5 ;
45) 9xy - 4a^2xy ;
49) -4 + 32a^3b^3 ;
53) -5x^3y^3 - 5x^3y^3 ;
57) ab(x - y)^3 + 8ab ;
61) x^2 + (a + b)xy + aby^2 ;
65) y^2 - (3b + 2a) xy + 6abx^2 ;
69) xy(a^2 + 2b^2) + ab( 2x^2 + y^2) ;
73) (xy + ab)^2 + (ay - bx)^2 ;
77) (xy - 3ab)^2 + (3ay + bx)^2 ;
5.
\(4x^5y^2+8x^4y^3+4x^3y^4=4x^3y^2(x^2+2xy+y^2)\)
\(=4x^3y^2(x+y)^2\)
9.
\(4x^5y^2+16x^4y^2-6x^3y^2=2x^3y^2(2x^2+4x-3)\)
13.
\(-3x^4y+6x^3y-3x^2y=-3x^2y(x^2-2x+1)=-3x^2y(x-1)^2\)
17.
\(8x^3-8x^2y+2xy^2=2x(4x^2-4xy+y^2)\)
\(=2x[(2x)^2-2.2x.y+y^2]=2x(2x-y)^2\)
21.
\((a^2+4)^2-16a^2b^2=(a^2+4)^2-(4ab)^2\)
\(=(a^2+4-4ab)(a^2+4+4ab)\)
25.
\(100a^2-(a^2+25)^2=(10a)^2-(a^2+25)^2\)
\(=(10a-a^2-25)(10a+a^2+25)\)
\(=-(a^2-10a+25)(a^2+10a+25)=-(a-5)^2(a+5)^2\)
29.
\(25a^2b^2-4x^2+4x-1=25a^2b^2-(4x^2-4x+1)\)
\(=(5ab)^2-(2x-1)^2=(5ab-2x+1)(5ab+2x-1)\)
33.
\(1-2m+m^2-x^2-4x-4=(m^2-2m+1)-(x^2+4x+4)\)
\(=(m-1)^2-(x+2)^2=[(m-1)-(x+2)][(m-1)+(x+2)]\)
\(=(m-x-3)(m+x+1)\)
37.
\(ax^2+bx^2+2xy(a+b)+ay^2+by^2\)
\(=x^2(a+b)+2xy(a+b)+y^2(a+b)\)
\(=(a+b)(x^2+2xy+y^2)=(a+b)(x+y)^2\)
41.
\(5a^2-5=5(a^2-1)=5(a^2-1^2)=5(a-1)(a+1)\)
45.
\(9xy-4a^2xy=xy(9-4a^2)=xy[3^2-(2a)^2]\)
\(=xy(3-2a)(3+2a)\)
49.
\(-4+32a^3b^3=4(8a^3b^3-1)=4[(2ab)^3-1^3]\)
\(=4(2ab-1)(4a^2b^2+2ab+1)\)
53.
\(-5x^3y^3-5x^3y^3=-10x^3y^3\)
57.
\(ab(x-y)^3+8ab=ab[(x-y)^3+8]=ab[(x-y)^3+2^3]\)
\(=ab(x-y+2)[(x-y)^2-2(x-y)+4]\)
\(=ab(x-y+2)(x^2+y^2-2xy-2x+2y+4)\)
61.
\(x^2+(a+b)xy+aby^2\)
\(=x^2+axy+bxy+aby^2=x(x+ay)+by(x+ay)\)
\(=(x+ay)(by+x)\)
65.
\(y^2-(3b+2a)xy+6abx^2\)
\(=y^2-3bxy-2axy+6abx^2\)
\(=y(y-3bx)-2ax(y-3bx)=(y-2ax)(y-3bx)\)
