a: \(-\left(x+1\right)^2-\left(x-1\right)^2\)
\(=-\left(x^2+2x+1\right)-\left(x^2-2x+1\right)\)
\(=-x^2-2x-1-x^2+2x-1\)
\(=-2x^2-2\)
b: \(\left(2x+1\right)^2+\left(2x-1\right)^2\)
\(=4x^2+4x+1+4x^2-4x+1\)
\(=8x^2+2\)
c: \(\left(3x+y\right)^2+\left(2x-y\right)^2\)
\(=9x^2+6xy+y^2+4x^2-4xy+y^2\)
\(=13x^2+2xy+2y^2\)
d: \(\left(x-4y\right)^2+\left(x+4y\right)^2\)
\(=x^2-8xy+16y^2+x^2+8xy+16y^2\)
\(=2x^2+32y^2\)
e: \(-\left(2x+3\right)-\left(5x-3\right)^2\)
\(=-2x-3-\left(25x^2-30x+9\right)\)
\(=-2x-3-25x^2+30x-9\)
\(=-25x^2+28x-12\)
a, $(x+1)^2 - (x-1)^2$
$= (x^2 + 2x + 1) - (x^2 - 2x + 1)$
$= x^2 + 2x + 1 - x^2 + 2x - 1$
$= -2x^2 - 2$
b, $(2x+1)^2 + (2x-1)^2$
$= 4x^2 + 4x + 1 + 4x^2 - 4x + 1$
$= 8x^2 + 2$
c, $(3x+y)^2 + (2x-y)^2$
$= 9x^2 + 6xy + y^2 + 4x^2 - 4xy + y^2$
$= 13x^2 + 2xy + 2y^2$
d, $(x-4y)^2 + (x+4y)^2$
$= x^2 - 8xy + 16y^2 + x^2 + 8xy + 16y^2$
$= 2x^2 + 32y^2$
e, $-(2x+3) - (5x-3)^2$
$= -2x - 3 - (25x^2 - 30x + 9)$
$= -2x - 3 - 25x^2 + 30x - 9$
$= -25x^2 + 28x - 12$
