Bài 1:
a: \(\left(3x-5\right)\left(3x+5\right)=\left(3x\right)^2-5^2=9x^2-25\)
b: \(\left(1-\frac23x\right)\left(\frac23x+1\right)=1^2-\left(\frac23x\right)^2=1-\frac49x^2\)
c: \(\left(2x^2-3\right)\left(2x^2+3\right)=\left(2x^2\right)^2-3^2=4x^4-9\)
d: \(\left(3x-\frac23\right)\left(\frac23+3x\right)=\left(3x\right)^2-\left(\frac23\right)^2=9x^2-\frac49\)
e: \(\left(5-\frac32x\right)\left(5+\frac32x\right)=5^2-\left(\frac32x\right)^2=25-\frac94x^2\)
f: (2x+3y)(2x-3y)\(=\left(2x\right)^2-\left(3y\right)^2=4x^2-9y^2\)
g: \(\left(5x+\frac12\right)\left(\frac12-5x\right)=\left(\frac12\right)^2-\left(5x\right)^2=\frac14-25x^2\)
Bài 2:
a: \(\left(x+10\right)^3=x^3+3\cdot x^2\cdot10+3\cdot x\cdot10^2+10^3\)
\(=x^3+30x^2+300x+1000\)
b: \(\left(2x+5\right)^3=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot5+3\cdot2x\cdot5^2+5^3\)
\(=8x^3+60x^2+150x+125\)
c: \(\left(\frac12x+3\right)^3=\left(\frac12x\right)^3+3\cdot\left(\frac12x\right)^2\cdot3+3\cdot\frac12x\cdot3^2+3^3\)
\(=\frac18x^3+\frac94x^2+\frac{27}{2}x+27\)
d: \(\left(x+4\right)^3=x^3+3\cdot x^2\cdot4+3\cdot x\cdot4^2+4^3=x^3+12x^2+48x+64\)
e: \(\left(3x+\frac12\right)^3=\left(3x\right)^3+3\cdot\left(3x\right)^2\cdot\frac12+3\cdot3x\cdot\left(\frac12\right)^2+\left(\frac12\right)^3\)
\(=27x^3+\frac{27}{2}x^2+\frac94x+\frac18\)
f: \(\left(5-x\right)^3=5^3-3\cdot5^2\cdot x+3\cdot5\cdot x^2-x^3=125-75x+15x^2-x^3\)
g: \(\left(2x-\frac32\right)^3=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot\frac32+3\cdot2x\cdot\left(\frac32\right)^2-\left(\frac32\right)^3\)
\(=8x^3-\frac92\cdot4x^2+6x\cdot\frac94-\frac{27}{8}=8x^3-18x^2+\frac{27}{2}x-\frac{27}{8}\)
h: \(\left(x-1\right)^3=x^3-3\cdot x^2\cdot1+3\cdot x\cdot1^2-1^3=x^3-3x^2+3x-1\)
k: \(\left(3x+\frac32\right)^3=\left(3x\right)^3+3\cdot\left(3x\right)^2\cdot\frac32+3\cdot3x\cdot\left(\frac32\right)^2+\left(\frac32\right)^3\)
\(=27x^3+\frac{81}{2}x^2+\frac{81}{4}x+\frac{27}{8}\)
l: \(\left(\frac25+5x\right)^3=\left(5x\right)^3+3\cdot\left(5x\right)^2\cdot\frac25+3\cdot5x\cdot\left(\frac25\right)^2+\left(\frac25\right)^3=125x^3+30x^2+\frac{12}{5}x+\frac{8}{125}\)
m: \(\left(\frac32-x\right)^3=\left(\frac32\right)^3-3\cdot\left(\frac32\right)^2\cdot x+3\cdot\frac32\cdot x^2-x^3\)
\(=\frac{27}{8}-\frac{27}{4}x+\frac92x^2-x^3\)
n: \(\left(x+\frac43\right)^3=x^3+3\cdot x^2\cdot\frac43+3\cdot x\cdot\left(\frac43\right)^2+\left(\frac43\right)^3\)
\(=x^3+4x^2+\frac{16}{3}x+\frac{64}{27}\)
