a)
\(20x^2-(5x-4)(4+5x)\\=20x^2-(5x-4)(5x+4)\\=20x^2-[(5x)^2-4^2]\\=20x^2-(25x^2-16)\\=20x^2-25x^2+16\\=-5x^2+16\)
b)
\((x-y)^2-x(x+2y)\\=x^2-2xy+y^2-x^2-2xy\\=-4xy+y^2\)
c)
\((x+3)^3(x-3)^3\\=[(x+3)(x-3)]^3\\=(x^2-3^2)^3\\=(x^2-9)^3\\=(x^2)^3-3\cdot (x^2)^2\cdot9+3\cdot x^2\cdot9^2-9^3\\=x^6-27x^4+243x^2-729\)
d)
\(x(x-1)(x+1)-(x-3)(x^2+3x+9)\\=x(x^2-1^2)-(x-3)(x^2+x\cdot3+3^2)\\=x^3-x-(x^3-3^3)\\=x^3-x-x^3+27\\=-x+27\\Toru\)
a: \(20x^2-\left(5x-4\right)\left(5x+4\right)\)
\(=20x^2-\left(25x^2-16\right)\)
\(=20x^2-25x^2+16=-5x^2+16\)
b: \(\left(x-y\right)^2-x\left(x+2y\right)\)
\(=x^2-2xy+y^2-x^2-2xy\)
\(=y^2-4xy\)
c: \(\left(x+3\right)^3\cdot\left(x-3\right)^3\)
\(=\left[\left(x+3\right)\left(x-3\right)\right]^3\)
\(=\left(x^2-9\right)^3\)
\(=x^6-27x^4+243x^2-729\)
d: \(x\left(x-1\right)\left(x+1\right)-\left(x-3\right)\left(x^2+3x+9\right)\)
\(=x\cdot\left(x^2-1\right)-\left(x^3-27\right)\)
\(=x^3-x-x^3+27=27-x\)