a: (2x+5)(4-3x)
=8x-6x^2+20-15x
=-6x^2-7x+20
b: (3xy+2x^2)*(-3x^2+xy)
=-9x^3y+3x^2y^2-6x^4+2x^3y
=-7x^3y+3x^2y^2-6x^4
c: (-1/2x^2y+6x)(1/2x^2y-2x)
=-1/4x^4y^2+x^3y+3x^3y-12x^2
=-1/4x^4y^2+4x^3y-12x^2
a) \(\left(2x+5\right)\left(4-3x\right)\)
\(=2x\left(4-3x\right)+5\left(4-3x\right)\)
\(=8x-6x^2+20-15x\)
\(=-6x^2+\left(8x-15x\right)+20\)
\(=-6x^2-7x+20\)
b) \(\left(3xy+2x^2\right)\left(-3x^2+xy\right)\)
\(=3xy\left(-3x^2+xy\right)+2x^2\left(-3x^2+xy\right)\)
\(=-9x^3y+3x^2y^2-6x^4+2x^3y\)
\(=3x^2y^2+\left(-9x^3y+2x^3y\right)-6x^4\)
\(=3x^2y^2-7x^3y-6x^4\)
c) \(\left(-\dfrac{1}{2}x^2y+6x\right)\left(-2x+\dfrac{1}{2}x^2y\right)\)
\(=-\dfrac{1}{2}x^2y\left(-2x+\dfrac{1}{2}x^2y\right)+6x\left(-2x+\dfrac{1}{2}x^2y\right)\)
\(=x^3y-\dfrac{1}{4}x^4y^2-12x^2+3x^3y\)
\(=\left(x^3y+3x^3y\right)-\dfrac{1}{2}x^4y^2-12x^2\)
\(=4x^3y-\dfrac{1}{2}x^4y^2-12x^2\)
