Question

How will you multiply \[ - 2{x^3}(3{x^2} + 4x + 5)\]?
\[
  A) 6{x^3} - 8{x^4} - 10{x^3} \\
  B) - 8{x^3} - 8{x^2} - 10{x^3} \\
  C) - 6{x^3} - 8{x^4} - 10{x^3} \\
  D) - 7{x^3} - 8{x^4} - 10{x^3} \\
 \]

Answer 1

Hint: In order to multiply two polynomials we need to multiply each term in one polynomial with each term in the other polynomial. Keep in mind that when we multiply two terms together we need to multiply the coefficient (numbers) and add the exponents. In case it required further simplification.

Complete step by step solution:
Firstly we will multiply each term of the first polynomial to every term of the second polynomial in order to find the product. In the above equation we need to distribute \[ - 2{x^3}\]
\[
   \Rightarrow - 2{x^3}(3{x^2} + 4x + 5) \\
   \Rightarrow - 6{x^3} - 8{x^4} - 10{x^3} \\
 \]
Now we need to combine the like terms but in this case there are no like terms so the answer is \[ - 6{x^3} - 8{x^4} - 10{x^3}\].

Hence the correct answer is option ‘C’.

Additional information: The order while multiplications can take place in any order in which each of first two terms is multiplied each of the second two terms. Remember the correctness of the solution is not affected by the order of terms in the final answer.

Notes: Remember in the above equation we have used distributive law of multiplication as it is used when we multiply two polynomials. Later on focus on combining like terms for reducing expected number of products in term. Lastly we need to write the decreasing order of their exponent.