Question

(x^3 − 3x^2 + 4) · (2x^3 + 3x^2 − 4x)

Answer 1

2x^6 - 3x^5 - 13x^4 + 20x^3 + 12x^2 - 16x

Explanation:

(x^3 − 3x^2 + 4) · (2x^3 + 3x^2 − 4x)

~Distribute

x^3 * 2x^3 + x^3 * 3x^2 + x^3 * -4x - 3x^2 * 2x^3 - 3x^2 * 3x^2 - 3x^2 * -4 + 4 * 2x^3 + 4 * 3x^2 + 4 * -4x

~Apply rules of minuses and plus signs

2x^(3)x^(3) + 3x^(3)x^(2) - 4x^(3)x - 3 * 2x^(3)x^(2) - 3 * 3x^(2)x^(2) + 3 * 4x^(2)x + 4 * 3x^(2) - 4 * 4x

~Simplify

2x^6 - 3x^5 - 13x^4 + 20x^3 + 12x^2 - 16x

Best of Luck!

Answer 2

• 2x^6 -3x^5 - 13x^4 + 20x^3 + 12x^2 - 16x

Explanation:

Multiplying and opening parenthesis

• (x^3 − 3x^2 + 4) · (2x^3 + 3x^2 − 4x) =
• x^3(2x^3) + x^3(3x^2) - x^3(4x) - 3x^2(2x^3) -3x^2(3x^2) + 3x^2(4x) + 4(2x^3) + 4(3x^2) - 4(4x) =
• 2x^6 + 3x^5 - 4x^4 - 6x^5 -9x^4 + 12x^3 + 8x^3 + 12x^2 - 16x =
• 2x^6 -3x^5 - 13x^4 + 20x^3 + 12x^2 - 16x