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\(a.9a^2-25b^4=\left(3a\right)^2-\left(5b^2\right)^2=\left(3a-5b^2\right)\left(3a+5b^2\right)\)
\(b.\left(2x+y\right)^2-1=\left(2x+y-1\right)\left(2x+y+1\right)\)
\(c.\left(x+y+z\right)^2-\left(x-y-z\right)^2=\left[\left(x+y+z\right)+\left(x-y-z\right)\right]\left[\left(x+y+z\right)\right]-\left(x-y-z\right)\\ =2x.\left(2y+2z\right)\)
a) \(9a^2-25b^4=\left(3a\right)^2-\left(5b^2\right)^2=\left(3a-5b^2\right)\left(3a+5b^2\right)\)
b) \(\left(2x+y\right)^2-1=\left(2x+y\right)^2-1^2=\left(2x+y+1\right)\left(2x+y-1\right)\)
c) \(\left(x+y+z\right)^2-\left(x-y-z\right)^2=\left(x+y+z+x-y-z\right)\left(x+y+z-x+y+z\right)\)
\(=2x\left(2y+2z\right)\)
a) (x+y)2 + (x-y)2 + 2(x+y)(x-y) = (x + y + x - y)2 = (2x)2
b) (x-y+z)2 + (y-z)2 + 2(x-y+z)(y-z) = (x-y+z+y-z)2 = x2
c) (x+y+z)2 - 2(x+y+z)(x+y) + (x+y)2 = (x+y+z-x-y)2 = z2