e) \(\left(x-y+z\right)^2+\left(y-z\right)^2+2\left(x-y+z\right)\left(y-z\right)\)
\(=\left(x-y+z\right)^2+2\left(x-y+z\right)\left(y-z\right)+\left(y-z\right)^2\)
\(=\left[\left(x-y+z\right)+\left(y-z\right)\right]^2\)
\(=\left(x-y+z+y-z\right)^2\)
\(=x^2\)
f) \(\left(5x+1\right)^2-\left(5x+3\right)\left(5x-3\right)\)
\(=25x^2+10x+1-\left(25x^2-9\right)\)
\(=25x^2+10x+1-25x^2+9\)
\(=10x+10\)
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