Multiplication of a Polynomial by a Monomial
We should multiply each term of the polynomial by the monomial and we should have to add the product –
Example–1) 5a ( 3a⁴b² - 2b⁴c² + 8b⁵a⁴)
Ans.) 5a ( 3a⁴b² - 2b⁴c² + 8b⁵a⁴)
= 5a X 3a⁴b² - 5a X 2b⁴c² + 5a X 8b⁵a⁴
= {(5 X 3 ) X a¹⁺⁴ b²} – {( 5 X 2 ) X ab⁴c² + {(5 X 8) X a⁴⁺¹ b⁵}
= 15 a⁵b² - 10 ab⁴c² + 40 a⁵b⁵ (Ans.)
2) 8bc ( 3a⁶b² - 2b²c² - 4b⁵a²)
Ans.) 8bc ( 3a⁶b² - 2b²c² - 4b⁵a²)
= (8bc X 3a⁶b²) – (8bc X 2b²c²) – (8bc X 4b⁵a²)
= {(8 X 3 ) X a⁶ b²⁺¹ c } – {( 8 X 2 ) X b²⁺¹ c²⁺¹} - {(8 X 4) X a² b⁵⁺¹ c }
= 24 a⁶bᶟc – 16 bᶟcᶟ - 32 a²b⁶c (Ans.)