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a)
\(1.24^2-0.24^2\\ =\left(\dfrac{31}{25}\right)^2-\left(\dfrac{6}{25}\right)^2\\ =\left(\dfrac{31}{25}-\dfrac{6}{25}\right)\left(\dfrac{31}{25}+\dfrac{6}{25}\right)=\dfrac{37}{25}\)
b)
\(\dfrac{1}{8}-8x^3\\ =\left(\dfrac{1}{2}\right)^3-\left(2x\right)^3\\ =\left(\dfrac{1}{2}-2x\right)\left(\dfrac{1}{4}+2x+4x^2\right)\)
c)
\(x^2-x+\dfrac{1}{4}\\ =x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2\\ =\left(x-\dfrac{1}{2}\right)^2\)
d)
\(x^2+x+\dfrac{1}{4}\\ =x^2+2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2\\ =\left(x+\dfrac{1}{2}\right)^2\)
a , \(16x^2+8x+1=\left(4x\right)^2+2.4x.1+1^2=\left(4x+1\right)^2\)
b , \(x^2-x+\dfrac{1}{4}=x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2=\left(x-\dfrac{1}{2}\right)^2\)
a,(4x+1)2 e,\(\left(\dfrac{3}{2}x-\dfrac{2}{5}\right)^2\)
b,(x-\(\dfrac{1}{2}\))2 g,\(\left(xy+1\right)^2\)
c,(\(x+\dfrac{3}{2}\))2 h,\(\left(x+5\right)^2\)
d,\(\left(x-\dfrac{5}{4}\right)^2\) i,\(-\left(x-6\right)^2\)
k,\(-\left(2x+3\right)^2\)
Bài 1:
a) -16 +(x-3)2
<=> (x-3)2-16
<=> (x-3)2 -42
<=> (x-3-4)(x-3+4)
<=> (x-7)(x+1)
b) 64+16y+y2
<=> y2 + 2.8.y + 82
<=> (y+8)2
c) \(\dfrac{1}{8}-8x^3\)
\(\Leftrightarrow\left(\dfrac{1}{2}\right)^3-\left(2x\right)^3\)
\(\Leftrightarrow\left(\dfrac{1}{2}-2x\right)\left(\dfrac{1}{4}+x+4x^2\right)\)
d)\(x^2-x+\dfrac{1}{4}\)
\(\Leftrightarrow x^2-2.\dfrac{1}{2}.x+\left(\dfrac{1}{2}\right)^2\)
\(\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2\)
e) x4 + 4x2 + 4
<=> (x2)2 + 2.2.x2 +22
<=> (x2 + 2)2
g)\(8x^3+60x^2y+150xy^2+125y^3\)
\(\Leftrightarrow\left(2x+5y\right)^3\)
a: \(=\dfrac{\left(2\cdot547+1\right)\cdot3}{547\cdot211}-\dfrac{546}{547\cdot211}-\dfrac{4}{547\cdot211}\)
\(=\dfrac{2735}{547\cdot211}=\dfrac{5}{211}\)
b: x=7 nên x+1=8
\(x^{15}-8x^{14}+8x^{13}-8x^{12}+...-8x^2+8x-5\)
\(=x^{15}-x^{14}\left(x+1\right)+x^{13}\left(x+1\right)-x^{12}\left(x+1\right)+...-x^2\left(x+1\right)+x\left(x+1\right)-5\)
\(=x^{15}-x^{15}-x^{14}+x^{14}-...-x^3-x^2+x^2+x-5\)
=x-5=7-5=2
a) x2 +4x+4 = ( x + 2 )2
b) 16x2 - 8xy + y2 = ( 4x - y )2
c)9a2 +16b2 - 24ab = ( 3a - 4y ) 2
d) x2 - x + \(\dfrac{1}{4}\)= ( x - \(\dfrac{1}{2}\))2
e) y2 + \(\dfrac{1}{2}y\) + \(\dfrac{1}{16}\) = ( y + \(\dfrac{1}{4}\))2
b,\(\dfrac{4}{9}x^2+4x+9=\left(\dfrac{2}{3}x\right)^2+2.\dfrac{2}{3}x.3+3^2=\left(\dfrac{2}{3}x+3\right)^2\)
c, \(x^3+9x^2+27x+27=x^3+3.x^2.3+3.x.3^2+3^3=\left(x+3\right)^3\)
d, \(\dfrac{1}{8}-\dfrac{3}{4}x+\dfrac{3}{2}x^2-x^3=\left(\dfrac{1}{2}\right)^3-3.\left(\dfrac{1}{2}\right)^2.x+3.\dfrac{1}{2}.x^2-x^3=\left(\dfrac{1}{2}-x\right)^3\)
TK MIK 
a/ \(\left(x+\dfrac{4}{3}y^2\right)^2\)
\(=x^2+2.x.\dfrac{4}{3}y^2+\left(\dfrac{4}{3}y^2\right)^2\)
\(=x^2+\dfrac{8}{3}xy^2+\dfrac{16}{9}y^4\)
b/ \(\left(2x^2+\dfrac{5}{3}y\right)^2\)
\(=\left(2x^2\right)^2+2.2x^2.\dfrac{5}{3}y+\left(\dfrac{5}{3}y\right)^2\)
\(=4x^4+\dfrac{20}{3}x^2y+\dfrac{25}{9}y^2\)
!!
b: \(=\left(\dfrac{1}{2}-2x\right)\left(\dfrac{1}{4}+x+4x^2\right)\)
c: \(=\left(x-\dfrac{1}{2}\right)^2\)
d: \(=\left(x+\dfrac{1}{2}\right)^2\)