# POLQ 1 | Lesson 1 | Explore (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.