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1) \(x^2\left(a-b\right)m-2xy\left(a-b\right)+ay^2-by^2=\left(a-b\right)x^2m-\left(a-b\right)2xy+\left(a-b\right)y^2=\left(a-b\right)\left(x^2m-2xy+y^2\right)\)
2) \(10a^3-10a=10a\left(a^2-1\right)=10a\left(a+1\right)\left(a-1\right)\)
3) \(16a^3xy-54b^3xy^4=2xy\left(8a^3-27b^3y^3\right)=2xy\left(2a-3by\right)\left(4a^2+6aby+9b^2y^2\right)\)
4) \(16+2x^3y^3=2\left(8+x^3y^3\right)=2\left(2+xy\right)\left(4+2xy+x^2y^2\right)\)
5) \(\left(a+b\right)^3+c^3=\left(a+b+c\right)\left(\left(a+b\right)^2+\left(a+b\right)c+c^2\right)=\left(a+b+c\right)\left(a^2+2ab+b^2+ac+bc+c^2\right)\)
Phân tích đa thức thành nhân tử ( phối hợp các phương pháp )
1) x2 - ( a + b )xy + aby2
\(=x^2-axy-bxy+aby^2\)
\(=(x^2-axy)-(bxy+aby^2)\)
\(=x(x-ay)-by(x+ay)\)
\(=(x-ay)(x-by)\)
2) x2 + ( 2a + b )xy + 2aby2
=x2 + 2axy + bxy + 2aby2
=(x2+ bxy) +(2axy+ 2aby2 )
=x(x+ by) +2ay(x+ by)
=(x+ by)(x+2ay)
1) \(xy\left(a^2+2b^2\right)-ab\left(2x^2+y^2\right)\)
\(=a^2xy+2b^2xy-2abx^2-aby^2\)
\(=\left(a^2xy-aby^2\right)+\left(2b^2xy-2abx^2\right)\)
\(=ay\left(ax-by\right)+2bx\left(by-ax\right)\)
\(=ay\left(ax-by\right)-2bx\left(ax-by\right)\)
\(=\left(ax-by\right)\left(ay-2bx\right)\)
2) Sửa đề \(\left(xy+ab\right)^2+\left(bx-ay\right)^2\)
\(=\left(xy\right)^2+2xyab+\left(ab\right)^2+\left(bx\right)^2-2xyab+\left(ay\right)^2\)
\(=x^2y^2+a^2b^2+b^2x^2+a^2y^2\)
\(=\left(x^2y^2+b^2x^2\right)+\left(a^2b^2+a^2y^2\right)\)
\(=x^2\left(b^2+y^2\right)+a^2\left(b^2+y^2\right)\)
\(=\left(b^2+y^2\right)\left(x^2+a^2\right)\)
3) \(\left(2xy+ab\right)^2+\left(2ay-bx\right)^2\)
\(=\left(2xy\right)^2+2.2xyab+\left(ab\right)^2+\left(2ay\right)^2-2.2xyab+\left(bx\right)^2\)
\(=4x^2y^2+4xyab+a^2b^2+4a^2y^2-4xyab+b^2x^2\)
\(=4x^2y^2+4a^2y^2+a^2b^2+b^2x^2\)
\(=4y^2\left(x^2+a^2\right)+b^2\left(a^2+x^2\right)\)
\(=\left(a^2+x^2\right)\left(4y^2+b^2\right)\)
1) \(xy\left(a^2+2b^2\right)-ab\left(2x^2+y^2\right)\)
\(=a^2xy+2b^2xy-2x^2ab-y^2ab\)
\(=\left(a^2xy-y^2ab\right)+\left(2b^2xy-2x^2ab\right)\)
\(=ay\left(ax-by\right)+2bx\left(by-ax\right)\)
\(=ay\left(ax-by\right)-2bx\left(ax-by\right)\)
\(=\left(ax-by\right)\left(ay-2bx\right)\)
2) Sửa đề \(\left(xy+ab\right)^2+\left(bx-ay\right)^2\)
\(=\left(xy\right)^2+2xyab+\left(ab\right)^2+\left(bx\right)^2-2xyab+\left(ay\right)^2\)
\(=x^2y^2+a^2b^2+b^2x^2+a^2y^2\)
\(=\left(x^2y^2+b^2x^2\right)+\left(a^2b^2+a^2y^2\right)\)
\(=x^2\left(b^2+y^2\right)+a^2\left(b^2+y^2\right)\)
\(=\left(b^2+y^2\right)\left(a^2+x^2\right)\)
3) \(\left(2xy+ab\right)^2+\left(2ay-bx\right)^2\)
\(=\left(2xy\right)^2+2.2xyab+\left(ab\right)^2+\left(2ay\right)^2-2.2xyab+\left(bx\right)^2\)
\(=4x^2y^2+a^2b^2+4a^2y^2+b^2x^2\)
\(=\left(4x^2y^2+b^2x^2\right)+\left(4a^2y^2+a^2b^2\right)\)
\(=x^2\left(4y^2+b^2\right)+a^2\left(4y^2+b^2\right)\)
\(=\left(4y^2+b^2\right)\left(a^2+x^2\right)\)
Giải:
\(16a^3xy-54b^3xy^4\)
\(=2xy\left(8a^3-27b^3y^3\right)\)
\(=2xy\left[\left(2a\right)^3-\left(3by\right)^3\right]\)
\(=2xy\left(2a-3by\right)\left[\left(2a\right)^2+\left(2a\right)\left(3by\right)+\left(3by\right)^2\right]\)
\(=2xy\left(2a-3by\right)\left(4a^2+6aby+9b^2y^2\right)\)
Vậy ...
\(16a^3xy-54b^3xy^4\)
\(=2xy\left(8a^3-27b^3y^3\right)\)
\(=2xy\left(2a-3by\right)\left(4a^2+6aby+9b^2y^2\right)\)
1)
\(x^2+4xy+4y^2-a^2+2ab-b^2\)
\(=(x^2+4xy+4y^2)-(a^2-2ab+b^2)\)
\(=(x+2y)^2-(a-b)^2\)
\(=(x+2y-a+b)(x+2y+a-b)\)
2)
\(m^2-6m+9-x^2+4xy-4y^2\)
\(=(m^2-6m+9)-(x^2-4xy+4y^2)\)
\(=(m-3)^2-(x-2y)^2\)
\(=[(m-3)-(x-2y)][(m-3)+(x-2y)]\)
\(=(m-3-x+2y)(m-3+x-2y)\)
3)
\(ax^2+bx^2+2axy+2bxy+ay^2+by^2\)
\(=a(x^2+y^2+2xy)+b(x^2+2xy+y^2)\)
\(=a(x+y)^2+b(x+y)^2\)
\(=(a+b)(x+y)^2\)
4)
\(ax^2+bx^2+6ax+6bx+9a+9b\)
\(=(ax^2+6ax+9a)+(bx^2+6bx+9b)\)
\(=a(x^2+6x+9)+b(x^2+6b+9)\)
\(=a(x+3)^2+b(x+3)^2=(a+b)(x+3)^2\)
5)
\(8a^2xy-18b^2xy\)
\(=2xy(a^2-9b^2)=2xy[a^2-(3b)^2]\)
\(=2xy(a-3b)(a+3b)\)
1, \(y^2+\left(3b+2a\right)xy+6abx^2\)
\(=y^2+3bxy+2axy+6abx^2\)
\(=y\left(y+3bx\right)+2ax\left(y+3bx\right)\)
= \(\left(y+2ax\right)\left(y+3bx\right)\)
2, \(ab\left(x-y\right)^2+8ab\)
=\(ab\left(x^2-2xy+y^2\right)+8ab\)
=\(ab\left(x^2-2xy+y^2+8\right)\)
3, \(x^2-\left(2a+b\right)+2aby^2\)
=\(x^2-2axy-bxy+2aby^{2^{ }}\)
=\(\left(x-by\right)\left(x-2ay\right)\)
4, \(xy\left(a^2+2b^2\right)+ab\left(x^2+y^2\right)\)
=\(a^2xy+2x^2ab+y^2ab+2b^2xy\)
=\(\left(ã+yb\right)\left(ay+2xb\right)\)
a) x^2 - 4 + ( x - 2 )^2
= ( x- 2 )(x + 2 ) + ( x- 2)^2
= ( x - 2 ) ( x + 2 + x - 2 )
= 2x (x-2)
b) x^3 - 2x^2 + x - xy^2
= x ( x^2 - 2x + 1 - y^2)
= x [ ( x - 1 )^2 - y^2 ]
= x(x - 1 - y)( x - 1 + y )
c) x^3 - 4x^2 - 12x + 27
= x^3 + 3x^2 - 7x^2 - 21x + 9x + 27
= x^2 ( x + 3 ) - 7x ( x+ 3 ) + 9(x + 3 )
Để hai lần nha
= ( x+ 3 )(x^2 - 7x + 9 )
\(x^2-4+\left(x-2\right)^2\)
\(=\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2\)
\(=\left(x-2\right)\left(x+2+x-2\right)\)
\(=2x\left(x-2\right)\)
hk tốt
^^
1) \(2xm^3-2x=2x\left(m^3-1\right)=2x\left(m-1\right)\left(m^2+m+1\right)\)
2 ) \(5xy-40a^3b^3xy=5xy\left(1-8a^3b^3\right)=5xy\left(1-2ab\right)\left(1+2a^3b^3+2ab\right)\)
3 ) \(-16a^2bx^3-54a^2b=-2a^2b\left(8x^3+27\right)=-2a^2b\left(2x+3\right)\left(4x^2-6x+9\right)\)
4 ) \(2\left(a+b\right)^3+16=2\left[\left(a+b\right)^3+8\right]=2\left(a+b+2\right)\left(a^2-2ab+b^2-2a-2b+2\right)\)
5 ) \(27xy+xy\left(a+b\right)^3=xy\left[27+\left(a+b\right)^3\right]=xy\left(3+a+b\right)\left(9-3a-3b+a^2+2ab+b^2\right)\)
Học tốt !