# How to solve product of two binomials

1
by nacely

2015-08-31T13:58:15+08:00
To solve the product of two binomials, you need to multiply it using distributive property.

For example:
(4x +3) (7 -3x)
4x · 7    =  28x
4x · -3x = -12x^2
+3 · 7   =  +21
+3 · -3x     = -9x

Then list them all.
28x -12x^2 +21 -9x
Combine like terms
=9x -12x^2 +21

Here is a useful method that I always use.
First, list all the numbers that you see at the first binomial vertically, make sure you double it.
4x
4x
+3
+3
Second, list all the numbers that you see at the last binomial vertically, make sure you double it also, next on the first binomial, and also make sure that it is not repeating line by line
4x  7
4x  -3x
+3  7
+3  -3x
Third, add the symbols. These includes the multiplication sign (algebra) and equal sign.
4x · 7     =
4x · -3x  =
+3 · 7     =
+3 · -3x  =
Fourth, solve it. Multiply the numerical coefficients and add the literal coefficient. If the signs are alike, the answer will be positive, if the signs are different, the answer will be negative.
4x · 7        =  28x
4x · -3x     = -12x^2
+3 · 7        =  +21
+3 · -3x     = -9x
Fifth, list all the product HORIZONTALLY.
28x -12x^2 +21 -9x
Lastly, combine like terms or numbers having the same literal coefficients.
9x -12x^2 +21

F - First
L - Last