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a) \(x^2-2=\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\)
b) \(y^3-13=\left(y-\sqrt{13}\right)\left(y^2+\sqrt{13}y+13\right)\)
c) \(2x^2-4=\left(\sqrt{2}x-2\right)\left(\sqrt{2}x+2\right)\)
d) \(\left(x-1\right)^3-\left(y+1\right)^3=\left(x-1-y-1\right)\left[\left(x-1\right)^2+\left(x-1\right)\left(y+1\right)+\left(y+1\right)^2\right]=\left(x-y-2\right)\left(x^2-2x+1+xy-y+x-1+y^2+2y+1\right)=\left(x-y-2\right)\left(x^2+y^2-x+y+xy+1\right)\)
a) 4x2+4x+1
= (2x+1)2
b) x2-16x+64
= (x-8)2
c) 4x2-9y2
= (2x+3y)(2x-3y)
d) ( x-3).(x^2+3x+9)
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) \(\left(3x+1\right)^2-\left(x+1\right)^2=\left(3x+1+x+1\right)\left(3x+1-x-1\right)\\ =\left(4x+2\right)\cdot2x=4x\left(2x+1\right)\)
\(a,=\left(x+4\right)^2\\ b,=\left(x-6\right)^2\\ c,=-\left(4x^2-4x+1\right)=-\left(2x-1\right)^2\\ d,=\left(x-1\right)^3\)
a. \(x^2-4x+4=x^2-2.x.2+2^2=\left(x-2\right)^2\)
b. \(x^2-4y^2=x^2-\left(2y\right)^2=\left(x-2y\right)\left(x+2y\right)\)
c. \(4x^2-4x+1=\left(2x\right)^2-2.2x.1+1^2=\left(2x-1\right)^2\)
d. \(x^3-3x^2+3x-1\)
\(=x^3-1^3-3x^2+3x\)
\(=\left(x-1\right)\left(x^2-x+1\right)-3x\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-x+1-3x\right)\)
\(=\left(x-1\right)\left(x^2-4x+1\right)\)
e. \(4x^2-9=\left(2x\right)^2-3^2=\left(2x-3\right)\left(2x+3\right)\)
g. \(4x^2+12xy+9y^2=\left(2x\right)^2+2.2x.3y+\left(3y\right)^2=\left(2x+3y\right)^2\)
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
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)\(x^2-\left(2+y\right)^2=\left(x-2-y\right)\left(x+2+y\right)\)
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 - ( a3 + 3a2b + 3ab2 + b3)
= - 3a2b - 3ab2- b3= -b (3a2 + 3ab +b2)
16) 4x^2 + 4x + 1
= (2x +1 )2
a. (a2 - b2)2 - (a2 + b2)2
= (a2 - b2 - a2 - b2)(a2 - b2 + a2 + b2)
= -2b2 . 2a2
b. a6 - b6
<=> (a3)2 - (b3)2
<=> (a3 - b3)(a3 + b3)
\(a,\left(a^2-b^2\right)^2-\left(a^2+b^2\right)^2\\ =a^4-2a^2b^2+b^4-a^4-2a^2b^2-b^4\\ =-4a^2b^2\)
\(b,a^6-b^6=a^2\left(a^3-b^3\right)=a^2\left(a-b\right)\left(a^2+ab+b^2\right)\)
\(e,8+\left(4x-3\right)^3\\ =\left(8+4x-3\right)\left[64-8\left(4x-3\right)+\left(4x-3\right)^2\right]\\ =\left(4x+5\right)\left(64-32x+24+16x^2-24x+9\right)\\ =\left(4x+5\right)\left(16x^2-56x+97\right)\)
\(g,81-\left(9-x^2\right)^2\\ =\left(9-9+x^2\right)\left(9+9-x^2\right)\\ =x^2\left(18-x^2\right)\left[=x^2\left(\sqrt{18}-x\right)\left(\sqrt{18}+x\right)\right]\)
Chỗ trong ngoặc nếu bạn chưa học căn thì ko cần ghi nha