a)  \(4x^2+20x+25=\left(2x+5\right)^2\)

b) \(x^2-6x+9=\left(x-3\right)^2\)

c) \(4x^2+12x+9=\left(2x+3\right)^2\)

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

c) \(36-12x+x^2=x^2-12x+36=x^2-6x-6x+36\)

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

\(x^4-y^4\)

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

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

\(4x^2+12x+9\)

\(=\left(2x\right)^2+2.2x.3+9\)

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

\(36-12x+x^2\)

\(=6^2-2.6.x+x^2\)

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

b: \(5x^2+6xy+y^2\)

\(=5x^2+5xy+xy+y^2\)

\(=5x\left(x+y\right)+y\left(x+y\right)\)

\(=\left(x+y\right)\left(5x+y\right)\)

c: \(x^2-7x+10=\left(x-2\right)\left(x-5\right)\)

d: \(4x^2+12x+9-y^2\)

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

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

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

b)  \(8x^3+12x^2+6x+1=\left(2x+1\right)^3\)

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

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

Bài 1:

\(a,=3x\left(3xy+5y-1\right)\\ b,=\left(z-2\right)\left(3z-5\right)\\ c,=\left(x+2y\right)^2-4z^2=\left(x+2y+2z\right)\left(x+2y-2z\right)\\ d,=x^2-3x+5x-15=\left(x-3\right)\left(x+5\right)\)

Bài 2:

\(a,\Leftrightarrow x\left(x-4\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\end{matrix}\right.\\ b,\Leftrightarrow2x+2-4x^2-12x=9\\ \Leftrightarrow4x^2+10x+7=0\\ \Leftrightarrow4\left(x^2+\dfrac{5}{2}x+\dfrac{25}{16}\right)+\dfrac{3}{4}=0\\ \Leftrightarrow4\left(x+\dfrac{5}{6}\right)^2+\dfrac{3}{4}=0\left(vô.lí\right)\\ \Leftrightarrow x\in\varnothing\\ c,\Leftrightarrow x^2-12x+36=0\\ \Leftrightarrow\left(x-6\right)^2=0\\ \Leftrightarrow x=6\)

a) `x^4+2x^3-4x-4`

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

`=(x^2-2)(x^2+2)+2x(x^2-2)`

`=(x^2-2)(x^2+2+2x)`

b) `x^3-4x^2+12x-27`

`=(x^3-27)-(4x^2-12x)`

`=(x-3)(x^2+3x+9)-4x(x-3)`

`=(x-3)(x^2+3x+9-4x)`

`=(x-3)(x^2-x+9)`

c) `xy-4y-5x+20`

`=y(x-4)-5(x-4)`

`=(y-5)(x-4)`

a) Ta có: \(x^4+2x^3-4x-4\)

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

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

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

b) Ta có: \(x^3-4x^2+12x-27\)

\(=\left(x-3\right)\left(x^2+3x+9\right)-4x\cdot\left(x-3\right)\)

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

c) Ta có: \(xy-4y-5x+20\)

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

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

a) \(x^2+12x+35\)

\(=x^2+5x+7x+35\)

\(=\left(x^2+5x\right)+\left(7x+35\right)\)

\(=x\left(x+5\right)+7\left(x+5\right)\)

\(=\left(x+5\right)\left(x+7\right)\)

b)\(x^2-x-56\)

\(=x^2+7x-8x-56\)

\(=\left(x^2+7x\right)-\left(8x+56\right)\)

\(=x\left(x+7\right)-8\left(x+7\right)\)

\(=\left(x+7\right)\left(x-8\right)\)

c)\(5x^2-x-4\)

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

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

\(=5x\left(x-1\right)+4\left(x-1\right)\)

\(=\left(x-1\right)\left(5x+4\right)\)

TL:

a)\(x^2+5x+7x+35\) 

 =\(x\left(x+5\right)+7\left(x+5\right)\) 

=\(\left(x+7\right)\left(x+5\right)\) 

b) \(x^2-x-56\)

  =\(x^2+7x-8x-56\) 

=\(x\left(x+7\right)-8\left(x+7\right)\) 

=\(\left(x-8\right)\left(x+7\right)\) 

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

=\(\left(2x^2+1\right)^2-4x^2\) 

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

.......................(tự lm)

hc tốt

\(4\times^4+81\)

\(=\left(2\times^2\right)^2+36\times^2+9^2-36\times^2\)

\(=\left(2\times^2+9\right)^2-36\times^2\)

\(=\left(2\times^2+9+36\times\right)\left(2\times^2+9-36\times\right)\)

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

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

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

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

\(=4x^2-\left(y^2-8y+16\right)\)

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

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