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Given \[{\text{(5 - 2x)}}\]and \[{\text{(4 + x)}}\]

In order to calculate the product of the polynomial proceed as in the way by multiplication of each and every term

Of one bracket to another bracket.

\[

{\text{ = (4 + x)}}{\text{.(5 - 2x)}} \\

{{ = (4 \times 5 + 4 \times ( - 2x) + x(5) + x( - 2x))}} \\

{\text{On simplifying we get,}} \\

{\text{ = (20 - 8x + 5x - 2}}{{\text{x}}^{\text{2}}}{\text{)}} \\

{\text{ = 20 - 3x - 2}}{{\text{x}}^{\text{2}}} \\

\]

When we find the product of any two polynomials, we just multiply each term of the first polynomial by each term of the second polynomial then simplify. When we find the product of two binomials, we can use a technique known as the FOIL method. FOIL is an acronym which stands for First, Outside, Inside and Last.