Câu 1:
a. \(\frac{1}{4}x^2-64\)
\(=\left(\frac{1}{2}x\right)^2-8^2\)
\(=\left(\frac{1}{2}x+8\right)\left(\frac{1}{2}x-8\right)\)
b. \(\frac{1}{27}+x^3\)
\(=\left(\frac{1}{3}\right)^3+x^3\)
\(=\left(\frac{1}{3}+x\right)\left(\frac{1}{9}-\frac{1}{3}x+x^2\right)\)
c. \(\left(a+b\right)^3-\left(a-b\right)^3\)
\(=\left(a^3+3a^2b+3ab^2+b^3\right)-\left(a^3-3a^2b+3ab^2-b^3\right)\)
\(=a^3+3a^2b+3ab^2+b^3-a^3+3a^2b+3ab^2+b^3\)
\(=6a^2b+2b^3\)
\(=2b\left(3a^2+b^2\right)\)
câu 3:
732-272=(73-27)(73+27)=46.100=4600
a. \(x^2-6x+9=0\)
\(\left(x-3\right)^2=0\)
\(\Leftrightarrow x-3=0\)
\(x=3\)
b. \(50x^2-2=0\)
\(2\left(25x^2-1\right)=0\)
\(2\left[\left(5x\right)^2-1^2\right]=0\)
\(2\left(5x+1\right)\left(5x-1\right)=0\)
\(\Leftrightarrow\)* \(5x+1=0\)
\(5x=-1\)
\(x=-\frac{1}{5}\)
* \(5x-1=0\)
\(5x=1\)
\(x=\frac{1}{5}\)
Câu 3:
\(73^2-27^2\)
\(=\left(73+27\right)\left(73-27\right)\)
\(=100.46\)
\(=4600\)
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