POLQ 1 | Lesson 1 | Explore (Generic Rectangles)

Generic Rectangles

Generic rectangles (similar to the area model) provide another strategy for multiplying polynomials.

Consider \((13)(426)\),  we can think of this as \((10+3)(400+20+6)\)

\(10\) \(3\)
\(400\) \(4000\) \(1200\)
\(20\) \(200\) \(60\)
\(6\) \(60\) \(36\)

Combining the parts:  6556

Generic rectangles can be used to multiply a monomial by a binomial:

Ex. \(3x(2x+7) = 6x^2+21x\)

\(2x\) 7
\(3x\) \(6x^2\) \(21x\)

They can also be used to multiply any polynomial by any polynomial such as the trinomial by binomial below:

\((x^2+3x+2)(x-1)\)

\(x\) \(-1\)
\(x^2\) \(x^3\) \(-x^2\)
\(3x\) \(3x^2\) \(-3x\)
\(2\) \(2x\) \(-2\)

\(x^3+3x^2+2x-x^2-3x-2 = x^3+2x^2-x-2\).  Notice that we need to add the red together as well as the purple to combine like terms.  Compare this again to the distributive property.  This method is a means of organizing your multiplication.


Go to Practice (Multiplying Polynomials: Generic Rectangles)