12) \(\sqrt{11+2\sqrt{30}}=\sqrt{\left(\sqrt{6}\right)^2+2.\sqrt{6}.\sqrt{5}+\left(\sqrt{5}\right)^2}\)

\(=\sqrt{\left(\sqrt{6}+\sqrt{5}\right)^2}=\sqrt{6}+\sqrt{5}\)

\(=\sqrt{6+2\cdot\sqrt{6}\cdot\sqrt{5}+5}\)

\(=\sqrt{\left(\sqrt{6}+\sqrt{5}\right)^2}=\sqrt{6}+\sqrt{5}\)

\(\Delta=27^2-4.168=57>0\)

pt có 2 nghiệm pb 

\(x=\dfrac{27\pm\sqrt{57}}{2}\)

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

Trả lời:

x² + 4x + 3

= ( x² + 2.x.2 + 2² ) - 1

= ( x + 2 )² - 1

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

= ( x + 1 ) ( x + 3 )

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

\(4x^2+4x+1-4\)

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

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

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

Trả lời:

4x² + 4x - 3

= [ ( 2x )² + 2.2x.1 + 1 ] - 4

= ( 2x + 1 )² - 4

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

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

x² - x - 12

= x² + 3x - 4x - 12

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

= (x - 4)(x + 3)

Trả lời:

x² - x - 12 

= x² - 4x + 3x - 12

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

= ( x + 3 ) ( x - 4 )

\(x^3-64x=x\left(x^2-64\right)=x\left(x-8\right)\left(x+8\right)\)

𝑥(𝑥−8)(𝑥+8)

Biểu thức này không phân tích được nhé.

\(64x^4+1\)

\(=64x^4+16x^2+1-16x^2\)

\(=\left(8x^2-4x+1\right)\left(8x^2+4x+1\right)\)

\(=9a^2b^2\left(2a-b\right)\)

18a³b² - 9a²b³

9a²b²(2a-b)

9a²b².(2a - b)

Đề sai nhé .Sửu lại

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

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

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

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