Question

x (x-2)(x+2)-(x-3)(x^2+3x+9)

(2x+7)(4x^2-14x+49)-2x (2x-1)(2x+1)

Answer 1

\(x\left(x-2\right)\left(x+2\right)-\left(x-3\right)\left(x^2+3x+9\right)\)

\(=\left(x^2-2x\right)\left(x+2\right)-\left(x-3\right)\left(x^2+3x+9\right)\)

\(=x^3+2x^2-2x^2-4x-x^3-3x^2-9x+3x^2+9x+27\)

\(=9x-4x+27=5x+27\)

\(\left(2x+7\right)\left(4x^2-14x+49\right)-2x\left(2x-1\right)\left(2x+1\right)\)

\(=\left(2x+7\right)\left(4x^2-14+49\right)-\left(4x^2-2x\right)\left(2x+1\right)\)

\(8x^3-28x+98x+28x^2-98+343-8x^3-4x^2+4x^2+2x\)

\(\left(98x-28x+2x\right)+343=72x+343\)