\(x^2+7x+12=x^2+3x+4x+12=x\left(x+3\right)+4\left(x+3\right)=\left(x+3\right)\left(x+4\right)=0\)
\(x^2+3x-18=0\Leftrightarrow x^2-3x+6x-18=x\left(x-3\right)+6\left(x-3\right)=\left(x+6\right)\left(x-3\right)=0\)
b) \(x^2-10x+16\)
\(=x^2-2x-8x+16\)
\(=x\left(x-2\right)-8\left(x-2\right)\)
\(=\left(x-2\right)\left(x-8\right)\)
c) \(x^2+6x+8\)
\(=x^2+2x+4x+8\)
\(=x\left(x+2\right)+4\left(x+2\right)\)
\(=\left(x+2\right)\left(x+4\right)\)
d) tươn tự c
e) \(x^2+3x-18=0\)
\(\Leftrightarrow x^2+6x-3x-18=0\)
\(\Leftrightarrow x\left(x+6\right)-3\left(x+6\right)=0\)
\(\Leftrightarrow\left(x+6\right)\left(x-3\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+6=0\\x-3=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-6\\x=3\end{cases}}}\)
Vậy ,...
f) \(8x^2+30x+7=0\)
\(\Leftrightarrow8x^2+28x+2x+7=0\)
\(\Leftrightarrow4x\left(2x+7\right)+\left(2x+7\right)=0\)
\(\Leftrightarrow\left(2x+7\right)\left(4x+1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}2x+7=0\\4x+1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{-7}{2}\\x=\frac{-1}{4}\end{cases}}}\)
Vậy ...
g) \(x^3-11x^2+30x=0\)
\(\Leftrightarrow x^3-5x^2-6x^2+30x=0\)
\(\Leftrightarrow x^2\left(x-5\right)-6x\left(x-5\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(x^2-6x\right)=0\)
\(\Leftrightarrow x\left(x-5\right)\left(x-6\right)=0\)
\(\Leftrightarrow x=0\)hoặc x=5 hoặc x=6
Vậy ...
j) \(202^2-54^2+256.352\)
\(=\left(202-54\right)\left(202+54\right)+256.352\)
\(=148.256+256.352\)
\(=256.\left(148+352\right)\)
\(=256.500\)
\(=128000\)
k) \(5+10+....+50\)
\(=\frac{\left[\left(50-5\right):5+1\right]\left(50+5\right)}{2}\)
\(=275\)
h) \(621^2-769.373-148^2\)
\(=\left(621-148\right)\left(621+148\right)-769.373\)
\(=473.796-769.373\)
\(=769.\left(473-373\right)\)
\(=76900\)
