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6 tháng 9 2018

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

2)\(4a^{201}\)

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

4)\(25-9y^2=\left(5-3y\right)\left(5+3y\right)\)

5)\(\left(a+1\right)^2-16=\left(a+1-16\right)\left(a+1+16\right)=\left(a-15\right)\left(a+17\right)\)

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

6 tháng 9 2018

7) (a+b)2-(a-b)2

\(\left(a^2+2ab+b^2\right)-\left(a^2-2ab+b^2\right)=4ab\)

8 ) a^2 + 2ax + x^2

( a + x )2

9) x^2 - 4x + 4

( x-2)2

10) x^2-6xy+9y^2

= (x - 3y )2

11) x^3+8

= (x+2)( x2 - 2x + 4 )

12) a^3 + 27b^3

= (a + 3b ) ( a2 - 3ab + 9b2 )

13) 27x^3 - 1 

= ( 3x -1 ) ( 9x2 + 3x +1)

14) 1/8 - b^3

= ( 1/2 - b ) ( 1/4 + 1/2b + b2)

15) a^3 - (a+b)3

= a3 - ( a+ 3a2b + 3ab+ b3)

= - 3a2b - 3ab2- b3= -b (3a2 + 3ab +b2)

16) 4x^2 + 4x + 1

= (2x +1 )2

10 tháng 9 2016

a) \(x^2-81=\left(x-9\right)\left(x+9\right)\)

b) \(4x^2-25=\left(2x-5\right)\left(2x+5\right)\)

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

d) \(x^2+6xy+9y^2=\left(x+3y\right)^2\)

e) \(6x-9-x^2=-\left(x^2-6x+9\right)=-\left(x-3\right)^2\)

f) \(x^2-4x^2+4y^2+4xy=\left(x^2+4xy+4y^2\right)-4x^2=\left(x+2y\right)^2-4x^2\\ =\left(x+2y+2x\right)\left(x+2y-2x\right)=\left(3x+2y\right)\left(2y-x\right)\)

g) \(\left(a+b\right)^3+\left(a-b\right)^3=\left(a+b+a-b\right)\left[\left(a+b\right)^2-\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)

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

h) \(\left(3x+1\right)^2-\left(x+1\right)^2=\left(3x+1+x+1\right)\left(3x+1-x-1\right)\\ =\left(4x+2\right)\cdot2x=4x\left(2x+1\right)\)

a: \(x^2+6xy+9y^2=\left(x+3y\right)^2\)

b: \(4a^4-4a^2b^2+b^4=\left(2a^2-b^2\right)^2\)

\(x^6-2x^3y+y^2=\left(x^3-y\right)^2\)

b: \(\left(x+y\right)^3-\left(x-y\right)^3\)

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

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

\(25x^4-10x^2y^2+y^4=\left(5x^2-y^2\right)^2\)

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

15 tháng 8 2018

mk ghi đáp án, ko phân tích đc thì IB mk

a) \(x^2+6xy+9y^2=\left(x+3y\right)^2\)

b) \(4a^4-4a^2b^2+b^4=\left(2a^2-b^2\right)^2\)

c)  \(x^6+y^2-2x^3y=\left(x^3-y\right)^2\)

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

e)  \(25x^4-10x^2y^2+y^4=\left(5x^2-y^2\right)^2\)

f) \(-a^2-2a-1=-\left(a+1\right)^2\)

g)  \(27b^3-8a^3=\left(3b-2a\right)\left(9b^2+6ab+4a^2\right)\)

h)  \(x^3+9x^2y+27xy^2+27y^3=\left(x+3y\right)^3\)

i) \(16x^2-9\left(x+y\right)^2=\left(x-3y\right)\left(7x+3y\right)\)

28 tháng 8 2023

1) \(3x\left(x-1\right)+5\left(x-1\right)\)

\(=\left(x-1\right)\left(3x+5\right)\)

2) \(4x(x-2y)-8y(2y-x)\)

\(=4x\left(x-2y\right)+8y\left(x-2y\right)\)

\(=\left(4x+8y\right)\left(x-2y\right)\)

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

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

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

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

\(=\left(a-b\right)\left(a+b\right)\left(x-1\right)\)

4) \(3x\left(x-a\right)+4a\left(a-x\right)\)

\(=3x\left(x-a\right)-4a\left(x-a\right)\)

\(=\left(x-a\right)\left(3x-4a\right)\)

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

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

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

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

6) \(3x\left(x-3\right)^2+9\left(3-x\right)^2\)

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

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

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

7) \(x\left(m-a\right)^2-y\left(a-m\right)^2\)

\(=x\left(a-m\right)^2-y\left(a-m\right)^2\)

\(=\left(x-y\right)\left(a-m\right)^2\)

8) \(6y^2\left(x-1\right)^2+9y\left(1-x\right)^2\)

\(=6y^2\left(x-1\right)^2+9y\left(x-1\right)^2\)

\(=\left(6y^2+9x\right)\left(x-1\right)^2\)

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

#Ayumu

17 tháng 8 2021

mình đánh máy vội nên sai mn đừng trả lời câu này nha !!!!

3 tháng 7 2018

a) \(A=8x^3+12x^2y+6xy^2+y^3=\left(2x+y\right)^3\)

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

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

d)  \(D=27+27y^2+9y^4+y^6=\left(3+y^2\right)^3\)

1 tháng 1 2022

a) = (x - 2)- y2

= (x - 2 - y)(x + 2 + y)

b) = (x^2 + 6x + 9) - (2y)^2

= (x + 3)2 - (2y)2

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

c) = (x - 3y)2 - 62

= (x - 3y - 6)(x - 3y + 6)