Theory:

Follow the steps to multiply the polynomials in the horizontal method:
  • First, write the \(2\) polynomials in a row separated by using a multiplication sign.
  • Multiply each term of the first polynomial with each term of the second polynomial.
  • In this, the product is obtained by combining and adding the like terms.
Example:
We learn how to multiply two binomials \(a + 5\) by \(a + 7\) using a horizontal method.
 
Consider the polynomials \(a + 5\) and \(a + 7\).
 
Separate the two polynomials using a multiplication sign.
 
= (a+5)×(a+7)
 
Multiply each term of the first polynomial with each term of the second polynomial.
 
=a×(a+7) +5×(a+7)
 
=a×a+a×7+5×a+5×7
 
Combine the like term.
 
=a2+7a+5a+35
 
=a2+12a+35
 
Therefore, the multiplication of the given polynomials is a2+12a+35.