1) Tính nhanh:

a/ \(174^2-74^2=\left(174+74\right)\left(174-74\right)=248.100=24800\)

b/ \(115^2-30.115+15^2=115^2-2.15.115+15^2=\left(115-15\right)^2=100^2\)

\(=10000\)

c/ \(49^2+102.49+51^2=49^2+2.51.49+51^2=\left(49+51\right)^2=100^2\)

\(=10000\)

3)

a) \(x^2-12y+36y^2\)

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

b)\(25x^2-49y^2=\left(5x-7y\right)\left(5x+7y\right)\)

c) \(27x^3+27x^2+9x+1=\left(3x+1\right)^3\)

=(x-5y)²

= x²+20x +100

= y² -14y+47

..........

1/ \(x^2-10xy+25y^2=\left(x-5y\right)^2\)

2/ \(x^2+20x+100\)

3/ \(y^2-14y+49\)

4/ \(16x^2+24xy+9y^2\)

5/ \(9x^2-42xy+49y^2\)

6/ \(25x^2+90x+81\)

7/ \(64x^2-48x+9\)

13 

25

234

81 

316

 nhớ cho mình 1 k

\(x^2+x+\dfrac{1}{4}=\left(x+\dfrac{1}{4}\right)^2\)

\(8x^3+27=\left(2x+3\right)\left(4x^2-6x+9\right)\)

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

câu 1 chỗ chấm là 2

câu 2 là 5

câu 3 là 4

câu 4 là 6

câu 5 là 5

câu 6 là 7

câu 7 là 4

câu 8 là 6

câu 9 là <

câu 10 là >

R A nh rảnh quớ bn ơi......rảnh đi hok đê.......Ai fan Noo tk mk ha.....I Love You forever, Noo.....

Câu 1 : 2.

Câu 2 : 5.

Câu 3 : 4.

Câu 4 : 6.

Câu 5 : 5.

Câu 6 : 7.

Câu 7 : 4.

Câu 8 : 6.

Câu 9 : <.

Câu 10 : >.

Câu 1 : 5

Câu 2 : 2

Câu 3 : 8

Câu 4 : 3

Câu 5 : 5

Câu 6 : 2

Câu 7 : 6

Câu 8 : 7

Câu 9 : 8

Câu 10 : <

1: 5

2: 2

3: 8

4: 3:

5: 5

6: 2

7: 6

8: 7

9: 8

10: <

~ Chúc bạn học tốt ~

7, \(27x^3+y^3=\left(3x+y\right)\left(9x^2-3xy+y^2\right)\)

8, \(8x^3-\frac{1}{125}y^3=\left(2x-\frac{1}{5}y\right)\left(4x^2+\frac{2}{5}xy+\frac{1}{25}y^2\right)\)

9, ĐK x >= 0 

\(x-2\sqrt{x}-3=x-3\sqrt{x}+\sqrt{x}-3\)

\(=\sqrt{x}\left(\sqrt{x}+1\right)-3\left(\sqrt{x}+1\right)=\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)\)

10, \(-4x^2-4x+10=-\left(4x^2+4x+1\right)+11\)

\(=-\left[\left(2x+1\right)^2-11\right]=-\left(2x+1-\sqrt{11}\right)\left(2x+1+\sqrt{11}\right)\)

11;12 xem lại đề

13, \(-x^3+6xy^2-12xy^2+8y^3=-\left(x^3-6xy^2+12xy^2-8y^3\right)=-\left(x-2y\right)^3\)

Trả lời:

7, \(27x^3+y^3=\left(3x+y\right)\left(9x^2-3xy+y^2\right)\)

8, \(8x^3-\frac{1}{125}y^3=\left(2x-\frac{1}{5}y\right)\left(4x^2+\frac{2}{5}xy+\frac{1}{25}y^2\right)\)

9, \(x-2\sqrt{x}-3\left(ĐK:x\ge0\right)\)

\(=x-3\sqrt{x}+\sqrt{x}-3=\sqrt{x}\left(\sqrt{x}-3\right)+\left(\sqrt{x}-3\right)=\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)\)

10, \(10-4x-4x^2=-\left(4x^2+4x-10\right)=-\left(4x^2+4x+1-11\right)=-\left[\left(2x+1\right)^2-11\right]\)

\(=-\left(2x+1\right)^2+11=-\left[\left(2x+1\right)^2-11\right]=-\left(2x+1-\sqrt{11}\right)\left(2x+1+\sqrt{11}\right)\)

11,sửa đề:  \(15x\left(x-3y\right)+20y\left(3y-x\right)=15x\left(x-3y\right)-20y\left(x-3y\right)=5\left(x-3y\right)\left(3x-4y\right)\)

12, \(25x^2-2=\left(5x-\sqrt{2}\right)\left(5x+\sqrt{2}\right)\)

13, sửa đề: \(-x^3+6x^2y-12xy^2+8y^3=-\left(x^3-6x^2y+12xy^2-8y^3\right)=-\left(x-2y\right)^3\)

chó điên

a) 9x⁴+16y⁶-24x²y³

=(3x²)²-2.3x².4y³+(4y³)²

=(3x²-4y³)²

b) 16x²-24xy+9y²

=(4x)²-2.4x.3y+(3y)²

=(4x-3y)²

c) 36x²-(3x-2)²

=(36x-3x+2)(36x+3x-2)

=(33x+2)(39x-2)

d) 27x³+54x²y+36xy²+8y³

=(3x)³+3.(3x)².2y+3.3x.(2y)²+(2y)³

=(3x+2y)³

e) y⁹-9x²y⁶+27x⁴y³-27x⁶

=(y³)³-3.(y³)².3x²+3.y³.(3x²)²-(3x²)³

=(y³-3x²)³

f) 64x³+1

= (4x)³+1³

=(4x+1)[(4x)²-4x.1+1²]

=(4x+1)(16x²-4x+1)

e) 27x⁶-8x³  *sửa đề*

=(3x²)³-(2x)³

=(3x²-2x)[(3x)²+3x².2x+(2x)²]

=(3x²-2x)(9x²+6x³+4x²)

~~~

1/ x^2 +4xy +4y^2 = (x +2y)^2

2/ -x^3 +9x^2 -27x+27= - (x^3 -9x^2+27x-27) = - (x-3)^3

3/ 8x^6 +36x^4y+54^2y^2+27y^3 = (2x^2+3y)^3

4/ x^3 - 6x^2y+12xy^2 -8y^3= (x-2y)^3

1) x² + 4xy + 4y² = ( x + 2y )²

2) - x³ + 9x² - 27x + 27 = ( 3 - x )²

3) 8x⁶ + 36x⁴y + 54x²y² + 27y³ = ( 2x² + 3y )³

4) x³ - 6x²y + 12xy² - 8y³ = ( x - 2y )³

5) x² + 4y² +1 - 4xy - 2x + 4y = ( x² - 2y - 1 )²

6) x² + y² + 4 + 2xy + 4x + 4y = ( x + y + 2 )²