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a: \(A=\left(a^2-9\right)\left(a^2+9\right)=a^4-81\)
b: \(=\left(a^2-25\right)\left(a+5\right)\)
\(=a^3+5a^2-25a-125\)
\(a.2\left(x-1\right)^2+\left(x+3\right)^2=3\left(x-2\right)\left(x+1\right)\)
\(\Leftrightarrow2x^2-4x+2+x^2+6x+9=3x^2-3x-6\)
\(\Leftrightarrow2x^2+x^2-3x^2-4x+6x+3x+2+9+6=0\)
\(\Leftrightarrow5x+17=0\)
\(\Leftrightarrow x=-\dfrac{17}{5}\)
KL.............
\(b.\left(x+2\right)^2-2\left(x-3\right)=\left(x+1\right)^2\)
\(\Leftrightarrow x^2+4x+4-2x+6=x^2+2x+1\)
\(\Leftrightarrow x^2-x^2+4x-2x-2x+4+6-1=0\)
\(\Leftrightarrow9=0\left(vôly\right)\)
KL..................
\(c.TươngTự\)
a: \(A=\left(a+b+c\right)^2+\left(a-b+c\right)^2+\left(a+b-c\right)^2+\left(b+c-a\right)^2\)
\(=2\left(a+c\right)^2+2b^2+\left(a+b-c\right)^2+\left(a-b-c\right)^2\)
\(=2\left(a+c\right)^2+2b^2+2\left(a-c\right)^2+2b^2\)
\(=2\left(a^2+2ac+c^2+a^2-2ac+c^2\right)+4b^2\)
\(=2\left(2a^2+2c^2\right)+4b^2\)
\(=4a^2+4b^2+4c^2\)
b: \(\left(a+b+c\right)^2+\left(a+b-c\right)^2-2\left(a+b\right)^2\)
\(=2\left(a+b\right)^2+2c^2-2\left(a+b\right)^2\)
\(=2c^2\)
