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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 !
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) \(\left(a+b\right)^3+c^3=\left(a+b+c\right)\left(\left(a+b\right)^2+\left(a+b\right)c+c^2\right)=\left(a+b+c\right)\left(a^2+2ab+b^2+ac+bc+c^2\right)\)
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) \(\left(2xy+ab\right)^2+\left(2ay-bx\right)^2\)
\(=\left(2xy\right)^2+2.2xyab+\left(ab\right)^2+\left(2ay\right)^2-2.2xyab+\left(bx\right)^2\)
\(=4x^2y^2+a^2b^2+4a^2y^2+b^2x^2\)
\(=\left(4x^2y^2+b^2x^2\right)+\left(4a^2y^2+a^2b^2\right)\)
\(=x^2\left(4y^2+b^2\right)+a^2\left(4y^2+b^2\right)\)
\(=\left(4y^2+b^2\right)\left(a^2+x^2\right)\)
\(-16a^4b^6-24a^5b^5-9a^6b^4\)
\(=-a^4b^4\left(16b^2+24ab+9a^2\right)\)
\(=-a^4b^4\left[\left(4b\right)^2+2\cdot4\cdot3\cdot ab+\left(3a\right)^2\right]\)
\(=-a^4b^4\cdot\left(3a+4b\right)^2\)
(a2+4)2 -16a2
=(a2 +4)2 - (4a)2
=(a2-4a+4)(a2+4a+4)
=(a-2)2(a+2)2
(a2+4)2 - 16a2 = (a4 + 8a2 + 16) - 16a2 = a4 - 8a2 + 16 = (a2 - 4)2 = [ ( a - 2) ( a + 2)]2 = (a-2)2(a+2)2
\(=x^2y^2+8xyab+16a^2b^2+4a^2y^2-8xyab+4b^2x^2\)
\(=x^2y^2+4a^2y^2+4b^2x^2+16a^2b^2\)
\(=\left(x^2y^2+4b^2x^2\right)+\left(4a^2y^2+16a^2b^2\right)\)
\(=x^2\left(4b^2+y^2\right)+4a^2\left(y^2+4b^2\right)\)
\(=\left(4b^2+y^2\right)\left(x^2+4a^2\right)\)
\(\left(xy+4ab\right)^2+4\left(ay-bx\right)^2\)
\(=x^2y^2+8abxy+16a^2b^2+4a^2y^2-8abxy+4b^2x^2\)
\(=x^2y^2+16a^2b^2+4a^2y^2+4b^2x^2\)
\(=\left(x^2y^2+4b^2x^2\right)+\left(16a^2b^2+4a^2y^2\right)\)
\(=x^2\left(y^2+4b^2\right)+4a^2\left(4b^2+y^2\right)\)
\(=\left(x^2+a^2\right)\left(4b^2+y^2\right)\)
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 ...
\(16a^3xy-54b^3xy^4\)
\(=2xy\left(8a^3-27b^3y^3\right)\)
\(=2xy\left(2a-3by\right)\left(4a^2+6aby+9b^2y^2\right)\)