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\(4x^2+4x+1\)
\(=\left(2x\right)^2+2.2x.1+1\)
\(=\left(2x+1\right)^2\)
\(1+12x+36x^2\)
\(=1+2.6x+\left(6x\right)^2\)
\(=\left(1+6x\right)^2\)
a) Ta có: \(\left(4x^2-12x+9\right)-1\)
\(=\left(2x-3\right)^2-1^2\)
\(=\left(2x-3-1\right)\left(2x-3+1\right)\)
\(=\left(2x-4\right)\left(2x-2\right)\)
\(=4\left(x-2\right)\left(x-1\right)\)
b) Ta có: \(\left(\frac{x^2}{4}+2xy+4y^2\right)-25\)
\(=\left[\left(\frac{x}{2}\right)^2+2\cdot\frac{x}{2}\cdot2y+\left(2y\right)^2\right]-5^2\)
\(=\left(\frac{x}{2}+2y\right)^2-5^2\)
\(=\left(\frac{x}{2}+2y-5\right)\left(\frac{x}{2}+2y+5\right)\)
c) Ta có: \(1+12x+35x^2\)
\(=35x^2+12x+1\)
\(=35x^2+5x+7x+1\)
\(=5x\left(7x+1\right)+\left(7x+1\right)\)
\(=\left(7x+1\right)\left(5x+1\right)\)
d) Ta có: \(9x^2-24xy+15y^2\)
\(=9x^2-9xy-15xy+15y^2\)
\(=9x\left(x-y\right)-15y\left(x-y\right)\)
\(=\left(x-y\right)\left(9x-15y\right)\)
\(=3\left(x-y\right)\left(3x-5y\right)\)
e) Ta có: \(25x^2-20xy+3y^2\)
\(=25x^2-15xy-5xy+3y^2\)
\(=5x\left(5x-3y\right)-y\left(5x-3y\right)\)
\(=\left(5x-3y\right)\left(5x-y\right)\)
f) Ta có: \(24x^4-10x^2y+y^2\)
\(=24x^4-4x^2y-6x^2y+y^2\)
\(=4x^2\left(6x^2-y\right)-y\left(6x^2-y\right)\)
\(=\left(6x^2-y\right)\left(4x^2-y\right)\)
câu đầu mình nghĩ là 4x2 mới đúng chắc bạn viết thiếu
4x2-12x+9=(2x-3)2
4x2+4x+1=(2x+1)2
1+12x+36x2=(6x+1)2
9x2-24xy+16y2=(3x-4y)2
x2/4+2xy+4y2=(x/2 + 2y)2
-x2+10x2y+y2? câu này bạn có úp sai đề không ta ?
Bài 1:
a) 25\(x^2\) - 0,09
= \(\left(5x\right)^2-0,3^2\)
= (5x - 0,3) (5x +0,3)
Bài 5:
a: \(=\left(2x-3\right)^2\)
b: \(=\left(2x+1\right)^2\)
c: \(=\left(6x+1\right)^2\)
d: \(=\left(3x-4y\right)^2\)
e: \(=\left(\dfrac{1}{2}x-2y\right)^2\)
f: \(=-\left(x-5\right)^2\)
a) \(4x^2-12x+9=\left(2x\right)^2-2\cdot2x\cdot3+3^2=\left(2x-3\right)^2\)
b) \(4x^2+4x+1=\left(2x\right)^2+2\cdot2x\cdot1+1^2=\left(2x+1\right)^2\)
c) \(1+12x+36x^2=1^2+2\cdot1\cdot6x+\left(6x\right)^2=\left(1+6x\right)^2\)
d) \(9x^2-24xy+16y^2=\left(3x\right)^2-2\cdot3x\cdot4y+\left(4y\right)^2=\left(3x-4y\right)^2\)
e) \(8x^3+1=\left(2x\right)^3+1^3=\left(2x+1\right)\left(4x^2+2x+1\right)\)
f) \(-8x^3+27=3^3-\left(2x\right)^3=\left(3-2x\right)\left(9+6x+4x^2\right)\)
\(A=\left(6x-3y\right)+\left(4x^2-4xy+y^2\right)\)
\(=3\left(2x-y\right)+\left(2x-y\right)^2\)
\(=\left(3+2x-y\right)\left(2x-y\right)\)
\(B=9x^2-\left(y^2-4y+4\right)\)
\(=9x^2-\left(y-2\right)^2\)
\(=\left(3x+y-2\right)\left(3x-y+2\right)\)
A = ( 6x - 3y ) + (4x2 - 4xy + y2 )
A = 3.( 2x - y) + [ ( 2x )2 - 2.2.x.y + y2 ]
A = 3.( 2x - y ) + ( 2x - y )2
A = ( 2x - y ).(3 + 2x - y )
B = 9x2 - ( y2 - 4y + 4 )
B = ( 3x )2 - ( y - 2 )2
B = ( 3x - y + 2 ).( 3x + y - 2 )
C = - 25x2 + y2 - 6y + 9
C = ( y2 - 2.3.y + 32 ) - ( 5x )2
C = ( y - 3 )2 - ( 5x )2
C = (y - 3 - 5x ).( y - 3 +5x )
D = x2 - 4x - y2 -- 8y - 12
D = ( x2 - 4x + 4 ) - 4 - y2 - 8y -12
D = ( x - 2.2x + 22 ) - ( y2 + 2.4.y + 42 )
D = ( x - 2 )2 - ( y + 4 )2
D = ( x - 2 + y + 4 ).( x - 2 - y - 4 )
D = ( x + y + 2 ).( x - y - 6 )
1. \(\left(5x-y\right)^2\)
2. \(\left(x^2-2y\right)^2\)
3. \(\left(3x^2-2y\right)^2\)
4. \(\left(9^2-2x^3\right)^2\)
1/ \(25x^2-10xy+y^2=\left(5x\right)^2-2.5xy+y^2=\left(5x-y\right)^2\)
2/\(x^4-4x^2y+4y^2=\left(x^2\right)^2-2.x^2.2y+\left(2y\right)^2=\left(x^2-2y\right)^2\)
3/\(9x^4-12x^2y+4y^2=\left(3x^2\right)^2-2.3x^2.2y+4y^2=\left(3x^2-2y\right)^2\)
4/\(9x^4-12x^5+4x^6=\left(3x^2\right)^2-2.3x^2.2x^3+\left(2x^3\right)^2=\left(3x^2-2x^3\right)^2\)
a) \(4x^2-12x+9=\left(2x\right)^2-2.2x.3+3^2=\left(2x-3\right)^2\)
b) \(4x^2+4x+1=\left(2x\right)^2+2.2x.1+1^2=\left(2x+1\right)^2\)
c) \(1+12x+36x^2=1^2+2.6x.1+\left(6x\right)^2=\left(1+6x\right)^2\)
d) \(9x^2-24xy+16y^2=\left(3x\right)^2-2.3x.4y+\left(4y\right)^2=\left(3x-4y\right)^2\)
f) \(-x^2+10x-25=-\left(x^2-10x+25\right)=-\left(x-5\right)^2\)
g) \(-16a^4b^6-24a^5b^5-9a^6b^4=-\left(16a^4b^6+24a^5b^5+9a^6b^4\right)\)
\(=-\left[\left(4a^2b^3\right)^2+2.4a^2b^3.3a^3b^2+\left(3a^3b^2\right)^2\right]\)
\(=-\left(4a^2b^3+3a^3b^2\right)^2\)
h) \(25x^2-20xy+4y^2=\left(5x\right)^2-2.5x.2y+\left(2y\right)^2\) \(=\left(5x-2y\right)^2\)
i) \(25x^4-10x^2y+y^2=\left(5x^2\right)^2-2.5x^2.y+y^2=\left(5x^2-y\right)^2\)