a) \(A=-\left(7x+5\right)^2-\left(3x-5\right)^2+\left(10-6x\right)\left(5+7x\right)\)
\(=-\left(7x+5\right)^2-\left(3x-5\right)^2+2\left(5-3x\right)\left(5+7x\right)\)
\(=-\left(7x+5\right)^2-\left(3x-5\right)^2-2\left(3x-5\right)\left(7x+5\right)\)
\(=-\left[\left(7x+5\right)^2+2\left(7x+5\right)\left(3x-5\right)+\left(3x-5\right)^2\right]\)
\(=-\left(7x+5+3x-5\right)^2\)
\(=-\left(10x\right)^2\)
\(=-100x^2\)
b) \(B=-\left(2x+y\right)\left(y^2+4x^2-2xy\right)+8x\left(x-2\right)\left(x+2\right)\)
\(=-\left(2x+y\right)\left(4x^2-2xy+y^2\right)+8x\left(x^2-4\right)\)
\(=-\left(8x^3+y^3\right)+8x^3-32x\)
\(=-8x^3-y^3+8x^3-32x\)
\(=-y^3-32x\)
c) \(C=-\left(x-1\right)\left(x+1\right)-\left(x-2\right)\left(x^2+2x+4\right)+x\left(x^2+x-2\right)\)
\(=-\left(x^2-1\right)-\left(x^3-8\right)+\left(x^3+x^2-2x\right)\)
\(=-x^2+1-x^3+8+x^3+x^2-2x\)
\(=9-2x\)
