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\(\left(xy+4ab\right)^2+4\left(ay-bx\right)^2\)
\(=x^2y^2+8abxy+16a^2b^2+4a^2y^2-8abxy+4b^2x^2\)
\(=x^2y^2+16a^2b^2+4a^2y^2+4b^2x^2\)
\(=\left(x^2y^2+4b^2x^2\right)+\left(16a^2b^2+4a^2y^2\right)\)
\(=x^2\left(y^2+4b^2\right)+4a^2\left(4b^2+y^2\right)\)
\(=\left(x^2+a^2\right)\left(4b^2+y^2\right)\)
\(\left(xy+4ab\right)^2+4\left(ay-bx\right)^2\)
\(=x^2y^2+2xy.4ab+4^2a^2b^2+4\left(a^2y^2-2aybx+b^2x^2\right)\)
\(=x^2y^2+8aybx+16a^2b^2+4a^2y^2-8aybx+4b^2x^2\)
\(=x^2y^2+16a^2b^2+4a^2y^2+4b^2x^2\)
\(=\left(x^2y^2+4b^2x^2\right)+\left(16a^2b^2+4a^2y^2\right)\)
\(=x^2\left(y^2+4b^2\right)+4a^2\left(4b^2+y^2\right)\)
\(=\left(y^2+4b^2\right)\left(x^2+4a^2\right)\)
1)) 3xy(a2+b2)-ab(x2+9y2) = 3a2xy+3b2xy-x2ab-9y2ab=(3a2xy-x2ab)+(3b2xy-9y2ab)=ax(3ay-xb)+3by(3ay-xb)=(ax+3by)(3ay-xb)
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) \(\left(2xy+ab\right)^2+\left(2ay-bx\right)^2\)
\(=\left(2xy\right)^2+2.2xyab+\left(ab\right)^2+\left(2ay\right)^2-2.2xyab+\left(bx\right)^2\)
\(=4x^2y^2+a^2b^2+4a^2y^2+b^2x^2\)
\(=\left(4x^2y^2+b^2x^2\right)+\left(4a^2y^2+a^2b^2\right)\)
\(=x^2\left(4y^2+b^2\right)+a^2\left(4y^2+b^2\right)\)
\(=\left(4y^2+b^2\right)\left(a^2+x^2\right)\)
a) \(2x-72x^3=2x\left(1-36x^2\right)=2x\left(1-6x\right)\left(1+6x\right)\)
f) \(4x^4+1=4x^4+4x^2+1-4x^2=\left(2x^2+1\right)^2-\left(2x\right)^2=\left(2x^2-2x+1\right)\left(2x^2+2x+1\right)\)
a) x3-2x2-x+2
=x(x2-1)+2(-x2+1)
=x(x2-1)-2(x2-1)
=(x2-1)(x-2)
b)
x2+6x-y2+9
=x2+6x+9-y2
=(x+3)2-y2
=(x+3-y)(x+3+y)
\(=x^2y^2+8xyab+16a^2b^2+4a^2y^2-8xyab+4b^2x^2\)
\(=x^2y^2+4a^2y^2+4b^2x^2+16a^2b^2\)
\(=\left(x^2y^2+4b^2x^2\right)+\left(4a^2y^2+16a^2b^2\right)\)
\(=x^2\left(4b^2+y^2\right)+4a^2\left(y^2+4b^2\right)\)
\(=\left(4b^2+y^2\right)\left(x^2+4a^2\right)\)