Question

What is the product of -5x^3 + 2x - 4 and 2x^3 - 4x^2 + 6?

Show your work and explain your answer. If you do not explain the steps of your work, you will not receive credit. Leave your answer in standard form.
Is the product of -5x^3 + 2x - 4 and 2x^3 - 4x^2 + 6 equal to the product of 2x^3 - 4x^2 + 6 and -5x^3 + 2x - 4? Explain your answer.

Answer 1

-10x⁶+20x⁵+4x⁴-46x³+16x²+12x-24

Explanation:

(-5x³ + 2x - 4)(2x³ - 4x² + 6)

= -10x⁶ + 4x⁴ - 8x³ + 20x⁵ - 8x³ + 16x² - 30x³ + 12x - 24

= -10x⁶+20x⁵+4x⁴-46x³+16x²+12x-24

(-5x³ + 2x - 4)(2x³ - 4x² + 6)

Is same as

(2x³ - 4x² + 6)(-5x³ + 2x - 4)

Because multiplication is commutative.

a×b = b×a