a, \(4x^2+12x+9=\left(2x+3\right)^2\)
b, \(\left(x-4\right)^2-25=\left(x-4\right)^2-5^2=\left(x-4-5\right)\left(x-4+5\right)=\left(x-9\right)\left(x+1\right)\)
c, \(x^3-64=x^3-4^3=\left(x-4\right)\left(x^2+4x+16\right)\)
d, \(y^3+125=y^3+5^3=\left(y+5\right)\left(y^2-5y+25\right)\)
e, \(\left(x^2+1\right)^2-6\left(x^2+1\right)+9=x^4+2x^2+1-6x^2-6+9\)
\(=x^4-4x^2+4=\left(x^2-2\right)^2\)
a, \(4x^2+12x+9\)
\(=4x^2+6x+6x+9=2x\left(2x+3\right)+3\left(2x+3\right)\)
\(=\left(2x+3\right)^2\)
b, \(\left(x-4\right)^2-25=\left(x-4\right)^2-5^2\)
\(=\left(x-4-5\right)\left(x-4+5\right)=\left(x-9\right)\left(x+1\right)\)
c, \(x^3-64=x^3-4^3=\left(x-4\right)\left(x^2+4x+16\right)\)
d, \(y^3+125=y^3+5^3=\left(y+5\right)\left(y^2+5y+25\right)\)
e, \(\left(x^2+1\right)^2-6\left(x^2+1\right)+9\)
\(=\left(x^2+1\right)^2-2.3\left(x^2+1\right)+3^2\)
\(=\left(x^2+1-3\right)^2=\left(x^2-2\right)^2\)
Chúc bạn học tốt!!!
a) \(4x^2+12x+9\)
\(=\left(2x\right)^2+2.2x.3+3^2\)
\(=\left(2x+3\right)^2\)
b) \(\left(x-4\right)^2-25\)
\(=\left(x-4\right)^2-5^2\)
\(=\left(x-4-5\right)\left(x-4+5\right)=\left(x-9\right)\left(x+1\right)\)
c) \(x^3-64=x^3-4^3\)
\(=\left(x-4\right)\left(x^2+4x+16\right)\)
d) \(y^3+125=y^3+5^3\)
\(=\left(y+5\right)\left(y^2+5y+25\right)\)
e) \(\left(x^2+1\right)^2-6\left(x^2+1\right)+9\)
\(=\left(x^2+1\right)^2-2.3.\left(x^2+1\right)+3^2\)
\(=\left(x^2+1-3\right)^2=\left(x^2-2\right)^2\)
