# Distributive Property to Multiply Polynomials

Multiplying polynomials requires using the distributive property. This means that every term in one factor has to be multiplied by every term in the other factor.

Consider the following:

$$(2x+1)(3x-2) = 2x(3x-2) +1(3x-2)$$

or $$6x^2-4x+3x-2$$ combining like terms:  $$6x^2-x-2$$

That method also works for polynomials:

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

$$= x^2(2x^2-x+2)+3x(2x^2-x+2)-1(2x^2-x+2)$$

$$=x^4-x^3+2x^2+6x^3-3x^2+6x-2x^2+x-2$$

$$=2x^4+5x^3-3x^2+7x-2$$

Try the following:

1)  $$(3x-2)(4x^2+3x-1)$$

2)  $$(x^2+2x-1)(2x^2-x+1)$$

Did you get:  $$12x^3+x^2-9x+2$$  and $$2x^4+3x^3-3x^2+3x-1$$

As you try on other strategies, think about what strategy works best.