a) \(\left(2x-1\right)^2-\left(3x+5\right)^2\)
\(=\left[\left(2x-1\right)-\left(3x+5\right)\right]\left[\left(2x-1\right)+\left(3x+5\right)\right]\)
\(=\left(2x-1-3x-5\right)\left(2x-1+3x+5\right)\)
\(=\left(-x-6\right)\left(5x+4\right)\)
\(=-5x^2-4x-30x-24\)
\(=-5x^2-34x-24\)
b) \(\left(4x-7\right)\left(7+4x\right)-\left(5x-2\right)^2\)
\(=\left[\left(4x\right)^2-7^2\right]-\left(25x^2-20x+4\right)\)
\(=16x^2-49-25x^2+20x-4\)
\(=-9x^2+20x-53\)
c) \(\left(5x+2\right)^2+\left(x-7\right)^2-\left(3x-2\right)\left(3x+2\right)\)
\(=25x^2-20x+4+x^2-14x+49-9x^2+4\)
\(=17x^2-34x+57\)
d) \(2x\left(3x-8\right)-\left(4x+1\right)\left(5x-4\right)-\left(x-5\right)^2\)
\(=6x^2-16x-\left(20x^2-16x+5x-4\right)-\left(x^2-10x+25\right)\)
\(=6x^2-16x-20x^2+16x-5x+4-x^2+10x-25\)
\(=-15x^2+5x-21\)
e) \(\left(x-3\right)^3+\left(x+2\right)\left(x^2-2x+4\right)\)
\(=\left(x^3-9x^2+27x-27\right)+\left(x^3+2^3\right)\)
\(=x^3-9x^2+27x-27+x^3+8\)
\(=2x^3-9x^2+27x-19\)
f) \(\left(2x+1\right)^3-\left(3x-1\right)\left(9x^2+3x+1\right)\)
\(=\left(8x^3+12x^2+6x+1\right)-\left[\left(3x\right)^3-1^3\right]\)
\(=8x^3+12x^2+6x+1-27x^3+1\)
\(=-19x^3+12x^2+6x+2\)
