a, \(100a^2-\left(a^2+25\right)^2=\left(10a\right)^2-\left(a^2+25\right)^2\)

\(=\left(10a-a^2-25\right)\left(10a+a^2+25\right)=-\left(a-5\right)^2\left(a+5\right)^2\)

b,\(-5\left(xy\right)^3-5\left(xy\right)^3=-10\left(xy\right)^3\)

c,\(16+2\left(xy\right)^3=2\left(2+xy\right)\left(4-2xy+x^2y^2\right)\)

a) \(=x^2+4xy+4y^2-y^2\)

\(=\left(x+2y\right)^2-y^2\)

\(=\left(x+2y+y\right)\left(x+2y-y\right)\)

\(=\left(x+3y\right)\left(x+y\right)\)

b) \(=2x^2-4xy-xy+2y^2\)

\(=2x\left(x-2y\right)-y\left(x-2y\right)\)

\(=\left(x-2y\right)\left(2x-y\right)\)

Bài 1:

\(1,Sửa:x^3-2x^2+x=x\left(x^2-2x+1\right)=x\left(x-1\right)^2\\ 2,=6\left(x^2+2xy+y^2\right)=6\left(x+y\right)^2\\ 3,=2y\left(y^2+4y+4\right)=2y\left(y+2\right)^2\\ 4,=5\left(x^2-2xy+y^2\right)=5\left(x-y\right)^2\)

Bài 2:

\(1,=x\left(x^2-64\right)=x\left(x-8\right)\left(x+8\right)\\ 2,=2y\left(4x^2-9\right)=2y\left(2x-3\right)\left(2x+3\right)\\ 3,=3\left(x^3-1\right)=3\left(x-1\right)\left(x^2+x+1\right)\)

Bài 3:

\(a,=5\left(x^2+2x+1-y^2\right)=5\left[\left(x+1\right)^2-y^2\right]=5\left(x-y+1\right)\left(x+y+1\right)\\ b,=3x\left(x^2-2x+1-4y^2\right)=3x\left[\left(x-1\right)^2-4y^2\right]\\ =3x\left(x-2y-1\right)\left(x+2y-1\right)\\ c,=ab\left(a-b\right)\left(a+b\right)+\left(a+b\right)^2\\ =\left(a+b\right)\left(a^2b-ab^2+a+b\right)\\ d,=2x\left(x^2-y^2-4x+4\right)=2x\left[\left(x-2\right)^2-y^2\right]\\ =2x\left(x-y-2\right)\left(x+y-2\right)\)

Bài 1;

1) \(x^3-2x-x=x\left(x^2-2x-1\right)\)

2) \(6x^2+12xy+6y^2=6\left(x^2+2xy+y^2\right)=6\left(x+y\right)^2\)

3) \(2y^3+8y^3+8y=10y^3+8y=2y\left(5y^2+4\right)\)

4) \(5x^2-10xy+5y^2=5\left(x^2-2xy+y^2\right)=5\left(x-y\right)^2\)

Bài 2:

1) \(x^3-64x=x\left(x^2-64\right)=x\left(x-8\right)\left(x+8\right)\)

2) \(8x^2y-18y=2y\left(4x^2-9\right)=2y\left(2x-3\right)\left(2x+3\right)\)

3) \(24x^3-3=3\left(8x^3-1\right)=3\left(2x-1\right)\left(4x^2+2x+1\right)\)

Bài 3:

1) \(5x^2+10x+5-5y^2=5\left(x^2+2x+1-y^2\right)=5\left[\left(x+1\right)^2-y\right]=5\left(x-y+1\right)\left(x+y+1\right)\)

2) \(3x^3-6x^2+3x-12xy^2=3x\left(x^2-2x+1-4y^2\right)=3x\left[\left(x-1\right)^2-\left(2y\right)^2\right]=3x\left(x-2y-1\right)\left(x+2y-1\right)\)

3) \(a^3b-ab^3+a^2+2ab+b^2=ab\left(a^2-b^2\right)+\left(a+b\right)^2=ab\left(a-b\right)\left(a+b\right)+\left(a+b\right)^2=\left(a+b\right)\left(a^2b-ab^2+a+b\right)\)

4) \(2x^3-2xy^2-8x^2+8xy=2x\left(x^2-y^2-4x+4y\right)=2x\left[\left(x-y\right)\left(x+y\right)-4\left(x-y\right)\right]=2x\left(x-y\right)\left(x+y-4\right)\)

\(9\left(x-3y\right)^2-25\left(2x+y\right)^2\)

\(=\left[3\left(x-3y\right)\right]^2-\left[5\left(2x+y\right)\right]^2\)

\(=\left(3x-9y\right)^2-\left(10x+5y\right)^2\)

\(=\left[3x-9y+10x+5y\right]\left[3x-9y-\left(10x+5y\right)\right]\)

\(=\left(13x-4y\right)\left(-7x-14y\right)\)

\(=-7\left(x+2y\right)\left(13x-4y\right)\)

9(x - 3y)² - 25(2x + y)²

= 3².(x - 3y)² - 5².(2x + y)²

= (3x - 9y)² - (10x + 5y)²

= (3x - 9y - 10x - 5y)(3x - 9y + 10x + 5y)

= (-7x - 14y)(13x - 4y)

= -7(x + 2y)(13x - 4y)

a: =(16x+20)^2-(10x+10)^2

=(16x+20-10x-10)(16x+20+10x+10)

=(26x+30)(6x+10)

=4(13x+15)(3x+5)

b: =(x-y+4-2x-3y+1)(x-y+4+2x+3y-1)

=(-x-4y+5)(3x+2y+3)

c: =[(x+1)^2-(x-1)^2][(x+1)^2+(x-1)^2]

=(x^2+2x+1-x^2+2x-1)(x^2+2x+1+x^2-2x+1)

=2(x^2+1)*4x

=8x(x^2+1)

a/ \(\left(x+3y\right)\left(2x-y\right)\)

b/ \(\left(x^2+2\right)\left(x^2-2\right)\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)

b/ \(x^8-16=\left(x^4+4\right)\left(x^4-4\right)\)

\(=\left[\left(x^4+4x^2+4\right)-4x^2\right]\left(x^2-2\right)\left(x^2+2\right)\)

\(=\left[\left(x^2+2\right)^2-4x^2\right]\left(x^2-2\right)\left(x^2+2\right)\)

\(=\left(x^2+2+2x\right)\left(x^2+2-2x\right)\left(x^2-2\right)\left(x^2+2\right)\)

Answer:

\(2x^3+4x^2y+2xy^2\)

\(= 2 x ( x ² + 2 x y + y ² )\)

\(= 2 x ( x + y ) ² \)

\( − 3 x ^4 y − 6 x ^3 y ^2 − 3 x ^2 y ^3 \)

\(=-3x^2y(x^2+2xy+y^2)\)

\(=-3x^2y(x+y)^2\)

\(4x^5y^2+8x^4y^3+4x^3y^4\)

\(=4x^3y^2.x^2+4x^3y^2.2xy+4x^3y^2.y^2\)

\(=4x^3y^2.(x^2+2xy+y^2)\)

\(=4x^3y^2.(x+y)^2\)

1/Tự chép lại đb nha :v

 =a² - 9b²+2ab+3a²-8b²-12ab+6ab-3b²-2a²+ab

= 2a²-3ab-20b²

= (2a²+5ab) - (8ab+20b²)

= a(2a+5b) - 4b(2a+5b)

=(2a+5b)(a-4b)

câu 2 tương tự nhé :)

a) 3a +3b -a²-ab

= 3.(a+b) -a.(a+b)=(3-a).(a+b)

b) x² +x +y²-y-2xy

=(x² - 2xy+y²) +(x-y)

=(x-y).(x-y+1)

c) -x² +7x -6

= -x² + x +6x-6

= x.(1-x) -6.(1-x) = (1-x).(x-6)

d) 5x³y -10x²y² +5xy³

= 5xy.(x² -2xy +y²) = 5xy.(x-y)²

e) 2x² +7x -15

= 2x² -3x +10x -15

=x.(2x-3) + 5.(2x-3)

=(2x-3).(x+5)

g) x² -2x +2y -xy

=x.(x-2)-y.(x-2)

=(x-y).(x-2)

h) bn go lai de ho mk dc k?