Multiplying Binomials

One way of multiplying a binomials is to use the distributive property.
Below is an example of what the procedure looks like when multiplying (4x + 3) and (6x + 2.)

(4x + 3)(6x + 2)

= 4x(6x + 2) + 3(6x + 2)

= (4x)(6x) + (4x)(2) + (3)(6x) + (3)(2)

= 24x² + 8x + 18x + 6

Combine like terms

= 24x² + 26x + 6

To multiply the two polynomials requires each term of one polynomial
to be multiplied by every term of the other polynomial.
Arranging the polynomials one on top of another so that the terms align vertically
will make it easier and less confusing to solve.


(2x + 5)
(7x + 4)

+ 8x + 20

14x² + 35x + 0


= 14x² + 43x + 20

Special Products

If you can identify a product as one of the special products
it will simplify the multiplication process.
The following is an example of squaring a binomial..

(7x + 3)²

= (7x + 3)(7x + 3)

= (7x)(7x) + (7x)(3) + (7x)(3) + (3)(3)

= 49x² + 21x + 21x + 9

Combine like terms

= 49x² + 42x + 9