d) \(\left(x^2-2xy-3y^2\right)\left(4x+5y\right)\)
\(=4x\left(x^2-2xy-3y^2\right)+5y\left(x^2-2xy-3y^2\right)\)
\(=4x^3-8x^2y-12xy^2+5x^2y-10xy^2-15y^3\)
\(=4x^3+\left(-8x^2y+5x^2y\right)+\left(-12xy^2-10xy^2\right)+15y^3\)
\(=4x^3-3x^2y-22xy^2+15y^3\)
f) \(\left(x+2\right)\left(x-2\right)-\left(2x-3\right)^2\)
\(=x^2-2^2-\left(4x^2-12x+9\right)\)
\(=x^2-4-4x^2+12x-9\)
\(=\left(x^2-4x^2\right)+12x-\left(4+9\right)\)
\(=-3x^2+12x-13\)
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