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EXPANSION OF A POLYNOMIAL WRITTEN IN FACTORED FORM

To multiply two factors together, you must multiply every term in both factors by every term in the other factor. If both factors are Binomial s, the acronym FOIL is used, which stands for First '''O'''uter '''I'''nner '''L'''ast, referring the terms that are multiplied together. For example, if you wished to expand (x+2)(2x-5), you would get 2x^2+4x-5x-10, or 2x^2-x-10


EXPANSION OF <MATH>(X+Y)^N</MATH>


See Also: Binomial theorem



When expanding (x+y)^n, a special relationship exists between the coefficients of the terms when written in order of descending powers of ''x'' and ascending powers of ''y''. The coefficients will be the numbers in the (''n'' + 1)-th row of Pascal's Triangle .

For example, when expanding (x+y)^6, the following is obtained:
:{\color{red}1}x^6+{\color{red}6}x^5y+{\color{red}15}x^4y^2+{\color{red}20}x^3y^3+{\color{red}15}x^2y^4+{\color{red}6}xy^5+{\color{red}1}y^6 \,


SEE ALSO