Algebra - Polynomials

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7. Perform the indicated operation and identify the degree of the result.

\[\left( {4{x^6} - 3x} \right)\left( {4{x^6} + 3x} \right)\]

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Start Solution

All we need to do is foil out the two polynomials. Here is the result of doing that.

\[\left( {4{x^6} - 3x} \right)\left( {4{x^6} + 3x} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{16{x^{12}} - 9{x^2}}}\] Show Step 2

Remember the degree of a polynomial is just the largest exponent in the polynomial and so the degree of the result of this operation is twelve.