Answer: [tex]\bold{a)\quad -2x^6+3x^4+3x^3-3x^2+11x+20\qquad b)\quad YES}[/tex]
Step-by-step explanation:
a)
[tex](-2x^6+x-5)(x^3-3x-4)\\\\\text{Use distributive Property to multiply:}\\-2x^3(x^3-3x-4)+x(x^3-3x-4)-5(x^3-3x-4)\\\\.\ -2x^6+2x^4+8x^3\\+\qquad \quad +x^4\qquad \quad -3x^2-4x\\+ \underline{\qquad \qquad \qquad -5x^3\quad \quad+15x+20}\\= -2x^6+3x^4+3x^3-3x^2+11x+20[/tex]
b)
When multiplying, the order doesn't matter: 2 × 3 = 3 × 2
This is referred to as "Commutative Property of Multiplication"
So, (-2x⁶+x-5)(x³-3x-4) = (x³-3x-4)(-2x⁶+x-5)
