\(a,x^2+7x+7y-y^2\)

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

\(=\left(x-y\right)\left(x+y\right)+7\left(x+y\right)\)

\(=\left(x+y\right)\left(x-y+7\right)\)

\(b,x^2-2x-9y^2+6y\)

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

\(=\left(x-3y\right)\left(x+3y\right)-2\left(x-3y\right)\)

\(=\left(x-3y\right)\left(x+3y-2\right)\)

\(c,x^2-xy+x^3-3x^{2y}+3x^{2y}-y^3\)

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

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

\(1,a^2-2a+1-b^2\)

\(=\left(a^2-2a+1\right)-b^2\)

\(=\left(a-1\right)^2-b^2\)

\(=\left(a-1-b\right)\left(a-1+b\right)\)       Khai triển thành hằng đẳng thức số 3 e  nhé.

\(2,x^2+2xy+y^2-81\)

\(=\left(x^2+2xy+y^2\right)-81\)

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

\(=\left(x+y-9\right)\left(x+y+9\right)\)Cái này cũng HĐT số 3 nè

\(3,x^2+6y-9-y^2\)

\(=-\left(y^2-6y+9\right)+x^2\)

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

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

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

\(5,4x^2+y^2-9-4xy\)

\(=\left(4x^2-4xy+y^2\right)-9\)

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

\(=\left(2x-y-3\right)\left(2x-y+3\right)\)

Học tốt

a)<=>

A,=(x+y)(x-y)=x^2-y^2

x=(-1/2)^5:(1/2)^4=-1/2

x^2=1/4

y=8^2/(-2)^5=-2

y^2=4

A=1/4-4=-15/4

\(a,x^2y-8x+xy-8=xy\left(x+1\right)-8\left(x+1\right)=\left(xy-8\right)\left(x+1\right)\\ b,=\left(x+3y\right)^2-9=\left(x+3y-3\right)\left(x+3y+3\right)\)

\(A=3x^2\left(2x^2-7x-2\right)-6x^2\left(x^2-4x-1\right)-3x^3+15\\ A=6x^4-21x^3-6x^2-6x^4+24x^3+6x^2-3x^3+15\\ A=15\left(đpcm\right)\)

\(Sửa:\left(6x^3-7x^2+2x\right):\left(2x+1\right)\\ =\left(6x^3+3x^2-10x^2-5x\right):\left(2x+1\right)\\ =\left[3x^2\left(2x+1\right)-5x\left(2x+1\right)\right]:\left(2x+1\right)\\ =3x^2-5x\)

`#3107`

`a.`

`4x^2 - 6x = 2x(2x - 3)`

`b.`

`9x^4y^3 + 3x^2y^4 = 3x^2y^2(3x^2y + y^2)`

`c.`

`x^3 - 2x^2 + 5x`

`= x(x^2 - 2x + 5)`

a) 4x² - 6x

= 2x(2x - 3)

b) 9x⁴y³ + 3x²y⁴

= 3x²y³(3x² + 3y)

c) x³ - 2x² + 5x

= x(x² - 2x + 5)

1. \(x^4-2x^2+1=\left(x^2-1\right)^2\)

2. \(x^2+5x+\dfrac{25}{4}=x^2+2.x.\dfrac{5}{2}+\left(\dfrac{5}{2}\right)^2=\left(x+\dfrac{5}{2}\right)^2\)

3. \(16x^2-8x+1=\left(4x-1\right)^2\)

4. \(x^2+x-y^2+y=\left(x-y\right)\left(x+y\right)+\left(x+y\right)=\left(x-y+1\right)\left(x+y\right)\)

5. \(\dfrac{1}{4}x^2-\dfrac{4}{9}y^2=\left(\dfrac{1}{2}x-\dfrac{2}{3}y\right)\left(\dfrac{1}{2}x+\dfrac{2}{3}y\right)\)

6. \(a^2-2ab+b^2-x^2=\left(a-b\right)^2-x^2=\left(a-b-x\right)\left(a-b+x\right)\)

7. \(4x^2-20x+25-y^2=\left(2x-5\right)^2-y^2=\left(2x-5-y\right)\left(2x-5+y\right)\)

Kết quả nè

1.(x^2-1)^2×(x^2+1)^2

2.(2x-5)^2÷4

3.(4x-1)^2

4.(x+y)^2×(x-y)

5.(1/4x-4/9y)×(1/4x+1/9y)

1.(x^2-1)^2=[(x-1).(x+1]^2

2). (x+5/2)^2

3). {4x-1)^2

\(a)\)

\(21\left(x+3\right)^3:\left(3x+9\right)^2\)

\(=[21\left(x+3\right)^3]:[3^2\left(x+3\right)^2]\)

\(=7\left(x+3\right):3\)

Thay vào ta được: \(7.\frac{\left(-6+3\right)}{3}=7.\left(-3\right):3=-7\)

\(b)\)

Thay vào ta được:

\(\left(2.2^2-5.2+3\right)^4:[\left(2.2-3\right)^3:\left(2-1\right)^2]\)

\(=\left(2.4-10+3\right)^4:[\left(4-3\right)^31^2]\)

\(=1^4:\left(1^3.1\right)\)

\(=1:1\)

\(=1\)

\(c)\)

Thay vào ta được:

\(36.10^4.7^3:\left(-6.10^3.7^2\right)\)

\(=-6.10.7\)

\(=-420\)