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A polynomial is an expression which contains both variables and constants. Polynomials can have one or more number of terms. If the polynomial has two terms then it is called as Binomial expression. Polynomial multiplication can be described through FOIL method, Distributive or Horizontal method, Grid method, Vertical method. FOIL method is used for the multiplication of Binomial expressions.

**Example 1**: Multiply the polynomials ( – 5x + 3) and x + 4

**Horizontal method**: ( – 5x + 3) . (x+ 4)

( – 5x + 3).x + ( – 5x + 3).4

(x) – 5x(x) + 3(x) + (4) – 5x(4) + 3(4)

- + 3x + 16 - 20x + 12

Combining like terms

+ 11 - 17x + 12

**Vertical method:**

– 5x + 3

x + 4

- 20x + 12

- + 3x

+11 - 17x + 12

**Example 2**: Multiply the polynomials ( + 5x +13) and (4 - 6x – 7)

**Grid method:**

-7 |
-35x |
-91 |

-6 |
-30 |
-78x |

4 |
20 |
52 |

Adding all the nine terms:

-7 + 4 - 35x - 30 + 20 - 91 - 78x + 52

4 + 20 - 7 - 30+ 52 - 35x - 78x – 91

On combining the like terms

4 + 14 + 15 - 113x – 91

Here Grid method or Horizontal method or Vertical method can be used. FOIL method is not applicable.