As emphasized previously, the distributive property proves important when carrying out multiplication operations. When you multiply a polynomial by an expression consisting of only one term, you apply the single term to each of the terms in the polynomial expression. Here is an example:

3x (4x + 2) | |

(3x)(4x) + 3x (2) | 3x applied to both of the terms in the binomial. |

12x^{2} + 6x | Completing the multiplications. |

When you work with binomial expressions, the same practice applies. You must apply both of the terms in the first expression to both of the terms in the second expression. A common form of binomial multiplication problem involves two binomials that add terms:

(x + 6)(x + 5) | Binomial expressions. |

x(x + 5)+ 6(x + 5) ... |

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