\(a,( 2x-y)(4x^2-2xy-y^2)\)
\(= 8x^3-4x^2y+2xy^2 −4x^2y+2xy^2−y^3\)
\(=8x^3+4xy^2−8x^2y−y^3\)
\(b, (6x^5y^2-9x^4y^3+15x^3y^4) : 3x^3y^2\)
\(= 6x^5y^2 -3x^3y^2-9x^4y^3 :3x^3y^2 +15x^3y^2 :3x^3y^2\)
= \(2x^2-3xy+5y^2\)
\(c, (2x^3-21x^2+67x-60): (x-5)\)
= \((2x^3-10x^2-11x^2+55x+12x-60):(x-5)\)
= \([2x^2(x-5)-11x(x-5)+12(x-5)] :(x-5)\)
= \((x-5)(2x^2-11x+12):(x-5)\)
= \(2x^2-11x+12\)
\(d, (x^4+2x^3+x-25): (x^2+5)\)
= \((𝑥^2+5)⋅𝑥^4+2(𝑥^2+5)⋅𝑥^3+𝑥(𝑥^2+5)−25(𝑥^2+5)\)
=\( 𝑥^6+5𝑥^4+2(𝑥^2+5)⋅𝑥^3+𝑥(𝑥^2+5)−25(𝑥^2+5)\)
= \(𝑥^6+5𝑥^4+2𝑥^5+10𝑥^3+𝑥(𝑥^2+5)−25(𝑥^2+5)\)
= \(𝑥^6+5𝑥^4+2𝑥^5+10𝑥^3+𝑥^3+5𝑥−25(𝑥^2+5)\)
= \(𝑥^6+5𝑥^4+2𝑥^5+10𝑥^3+𝑥^3+5𝑥−25𝑥^2−125\)
= \(𝑥^6+5𝑥^4+2𝑥^5+11𝑥^3+5𝑥−25𝑥^2−125\)
= \(𝑥^6+2𝑥^5+5𝑥^4+11𝑥^3−25𝑥^2+5𝑥−125\)
\(d, (27x^3-8): (6x+9x^2+4)\)
= \((27𝑥^3−8)(9𝑥^2+6𝑥+4)\)
= \(27(9𝑥^2+6𝑥+4)⋅𝑥^3−8(9𝑥^2+6𝑥+4)\)
= \(243𝑥^5+162𝑥^4+108𝑥^3−8(9𝑥^2+6𝑥+4)\)
= \(243𝑥^5+162𝑥^4+108𝑥^3−72𝑥^2−48𝑥−32\)
