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# Polynomials 06: Multiplying Binomials

In this lesson we will look at multiplying binomials. The same principles apply as with monomials but it does become a bit more difficult. The most important rule is that each term MUST be multiplied by every other term in the other polynomial.

The acronym that is often used for a binomial multiplied by a binomial is FOIL (First Outer Inner Last). This means that you need to multiply the first term from each polynomial, the terms that are closest to the outside, the terms that are closest to the inside, and then the terms which are last. Of course it must be simplified where possible before finishing.

Example:
$(x + 4)(x+3)$
The First terms are $x * x = x^2$
The Outer terms are $x * (+3) = 3x$
The Inner terms are $(+4) * x = 4x$
The Last terms are $(+4) * (+3) = 12$

These are now combined to be $x^2+3x+4x+12$
which is simplified to the trinomial $x^2+7x+12$.

Being able to multiply polynomials is a very important foundation skill for working with quadratics, and quadratics have many very practical uses in real life such as calculating the flight path of objects, designing arches in construction, and even finding the best price to sell items in a store.

The FOIL acronym does not work for multiplying binomials by larger polynomials but the principle is the same.

Example:
$(x+2)(y-3x+5)$
1st * 1st: $x*y=xy$
1st * 2nd: $x*(-3x)=-3x^2$
1st * 3rd: $x*(+5)=5x$
2nd * 1st: $(+2)*y=2y$
2nd * 2nd: $(+2)*(-3y)=-6x$
2nd * 3rd: $(+2)*(+5)=10$
$xy-3x^2+5x+2y-6x+10$
$-3x^2+xy-x+2y+10$

This method can be used to multiply any polynomial by any polynomial. The order in which you multiply terms does not matter since you will simplify in the end but if you do not have a clear pattern it is very easy to miss a term.

Directions for this Lesson:
Watch the video below and complete the practice questions.

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