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

TL:

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

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

\(=3x.\left(x+2\right)\) 

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

~Study well~ :)

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

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

a, \(x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2-\dfrac{9}{4}\)

\(=\left(x-\dfrac{1}{2}\right)^2-\dfrac{3}{2}^2\)

\(=\left(x-\dfrac{1}{2}-\dfrac{3}{2}\right)\left(x-\dfrac{1}{2}+\dfrac{3}{2}\right)\)

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

b, \(x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2-\dfrac{1}{4}-2\)

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

\(=\left(x-\dfrac{1}{2}\right)^2-\dfrac{3}{2}^2\)

\(=\left(x-\dfrac{1}{2}-\dfrac{3}{2}\right)\left(x-\dfrac{1}{2}+\dfrac{3}{2}\right)\)

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

Chúc bạn học tốt!!!

\(\frac{2}{xy}:\left(\frac{1}{x}-\frac{1}{y}\right)^2-\frac{x^2+y^2}{\left(x-y\right)^2}\)

\(=\frac{2}{xy}:\left(\frac{y-x}{xy}\right)^2-\frac{x^2+y^2}{\left(x-y\right)^2}\)

\(=\frac{2}{xy}:\frac{\left(x-y\right)^2}{x^2y^2}-\frac{x^2+y^2}{\left(x-y\right)^2}\)

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

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

\(=-\frac{\left(x-y\right)^2}{\left(x-y\right)^2}=-1\)

a: =4x^2+8x-3x-6

=4x(x+2)-3(x+2)

=(x+2)(4x-3)

b: =3(3x^2-2x-1)

=3(3x^2-3x+x-1)

=3(x-1)(3x+1)

c: =2x^2-4x+x-2

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

=(x-2)(2x+1)

d: =3x^2+3x-2x-2

=3x(x+1)-2(x+1)

=(x+1)(3x-2)

e: =3x^2+9x+x+3

=3x(x+3)+(x+3)

=(x+3)(3x+1)

a) \(4x^2+5x-6\)

\(=4x^2+8x-3x-6\)

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

\(=4x\left(x+2\right)-3\left(x+2\right)\)

\(=\left(x+2\right)\left(4x-3\right)\)

b) \(9x^2-6x-3\)

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

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

\(=3\left[3x\left(x-1\right)+\left(x-1\right)\right]\)

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

c) \(2x^2-3x-2\)

\(=2x^2-4x+x-2\)

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

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

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

d) \(3x^2+x-2\)

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

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

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

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

e) \(3x^2+10x+3\)

\(=3x^2+9x+x+3\)

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

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

\(1,\)

\(x^2+x-12\)

\(=x^2-3x+4x-12\)

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

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

\(2,\)
\(x^2-9x+20\)

\(=x^2-4x-5x+20\)

\(=x\left(x-4\right)-5\left(x-4\right)\)

\(=\left(x-5\right)\left(x-4\right)\)

\(3,\)

\(x^2+x-20\)

\(=x^2-4x+5x-20\)

\(=x\left(x-4\right)+5\left(x-4\right)\)

\(=\left(x+5\right)\left(x-4\right)\)

c ) \(x^2-7x+12\)

\(=\left(x^2-3x\right)-\left(4x-12\right)\)

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

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

d ) \(x^2+7x+12\)

\(=\left(x^2+3x\right)+\left(4x+12\right)\)

\(=x\left(x+3\right)+4\left(x+3\right)\)

\(=\left(x+4\right)\left(x+3\right)\)

a ) \(x^2-5x+6\)

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

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

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

b )\(x^2+5x+6\)

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

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

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

a.x^2 - 5x + 6

=x²-2x-3x+6

=x(x-2)-3(x-2)

=(x-3)(x-2)

b.x^2 + 5x + 6

=x²+3x+2x+6

=x(x+3)+2(x+3)

=(x+2)(x+3)

a) 9  -(x-y)²

= 3² - (x-y)²

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

b) (x² +4)² - 16x²

= (x²+4)² - (4x)²

= (x² + 4 -4x).(x² + 4 +4x)

      \(9-\left(x-y\right)^2\)

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

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

      \(\left(x^2+4\right)^2-16x^2\)

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

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

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

a) 9 - ( x - y ) ^2

= 3 ^ 2 - ( x - y ) ^2

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

b) (x ^ 2 + 4 ) ^ 2 - 16x ^2

= (x ^ 2 + 4 ) ^ 2 - ( 4x ) ^2

= ( x ^ 2 + 4 - 4x )( x ^ 2 +4 +4x)

k cho mk na ^.^

x² + x -12 = x² + 4x - 3x - 12 = x(x+4) - 3(x+4) = (x+4)(x-3)

\(x^2+x-12\)

\(=x^2+x+\frac{1}{4}-\frac{49}{4}\)

\(=\left(x+\frac{1}{2}\right)^2-\left(\frac{7}{2}\right)^2\)

\(=\left(x+\frac{1}{2}-\frac{7}{2}\right)\left(x+\frac{1}{2}+\frac{7}{2}\right)\)

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