In the given problem, apply your knowledge in algebraic expression and basic mathematics specially in solving polynomials.
Multiplication of Polynomials
(y³ - y + 4)(3y² - 1)
3y⁵ - y³ - 3y³ - y + 12y² - 4
= 3y⁵ - 4y³ + 11y² - 4
(2d³ - 2d² + 4)(5d² - 2d + 1)
10d⁵ - 4d⁴ + 2d³ - 10d⁴ + 4d³ - 2d² + 10d² - 8d + 4
= 10d⁵ -14d⁴ + 6d³ + 8d² - 8d + 4
(5x³ - x)(2x⁴ + x² + 2x - 2)
10x⁷ + 5x⁵ + 10x⁴ - 10x³ - 2x⁵ - x³ - 2x² + 2x
= 10x⁷ + 3x⁵ + 10x⁴ - 11x³ - 2x² + 2x
(3b² + b - 2)(2b³ - 2b² - 7)
6b⁵ - 6b⁴ - 21b² + 2b⁴ - 2b³ - 7b - 4b³ - 4b² + 14
= 6b⁵ - 4b⁴ - 6b³ - 25b² - 7b + 14
(y⁴ + y³)³
(y⁴ + y³)³ = (y⁴ + y³)(y⁴ + y³)(y⁴ + y³)
(y⁴ + y³)(y⁴ + y³) = y⁸ + 2y³y⁴ + y⁶
(y⁴ + y³)(y⁸ + 2y³y⁴ + y⁶)
y¹² + 2y³y⁸ + y¹⁰ + y¹¹ + 2y⁶y⁴ + y⁹
= y¹² + y¹¹ + y¹⁰ + 2y³y⁸ + 2y⁶y⁴ + y⁹
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