a)   \(45+x^3-5x^2-9x\)

\(\Leftrightarrow\left(45-9x\right)+\left(x^3-5x^2\right)\)

\(\Leftrightarrow-9\left(x-5\right)+x^2\left(x-5\right)\) 

\(\Leftrightarrow\left(x-5\right)\left(x-3\right)\left(x+3\right)\) 

TK NKA !!!

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\(x^8+3x^4+4\)

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

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

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

\(4x^4+4x^3+5x^2+2x+1\)

\(=\left(4x^4+2x^3+2x^2\right)+\left(2x^3+x^2+x\right)+\left(2x^2+x+1\right)\)

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

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

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

b, \(\left(5x-2\right)^2=\left(5x-2\right)\left(5x-2\right)=\left[\left(5x-2\right)5x-\left(5x-2\right)2\right]=5x^2-10x+25\)

b, \(8^2-12x^2=\left(8^2-12x^2\right)\left(8^2+12x^2\right)\)

đúng ko :) 

@No name: Bị sai rồi nhé, a,b,c sai hết  :>

a) ( 4x + 5 )² 

= ( 4x )² + 2.4x.5 + 5² 

= 16x² + 40x + 25 

b) ( 5x - 2 )² 

= ( 5x )² - 2.5x.2 + 2² 

= 25x² - 20x + 4 

c) 8² - 12x² 

= 64 - 12x² 

= ( V8 - V12x )( V8 + V12x ) 

\(x^3-2x^2+5x\)

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

Ta có:\(2x^3-x^2+5x+3=2x^3+x^2-2x^2-x+6x+3=2x^2\left(x+0,5\right)-2x\left(x+0,5\right)+6\left(x+0,5\right)=\left(2x^2-2x+6\right)\left(x+0,5\right)\)

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

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

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

\(2\left(x-1\right)\left(x^2+\frac{3}{2}x-2\right)=2\left(x-1\right)\left\{\left(x^2+\frac{2x.3}{4}+\frac{9}{16}\right)-\left(2+\frac{9}{16}\right)\right\}\)

\(2\left(x-1\right)\left\{\left(x+\frac{3}{4}\right)^2-\left(2+\frac{9}{16}\right)\right\}=2\left(x-1\right)\left\{\left(x+\frac{3}{4}-2-\frac{9}{16}\right)\left(x+\frac{3}{4}+2+\frac{9}{16}\right)\right\}\)

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

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

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

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

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

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