   SEARCH HOME Math Central Quandaries & Queries  Question from chloe, a student: Expand and Simplify (3x+5)(5x-9) Hi Chloe,

The expansion uses the distributive law of multiplication over addition

$a (b + c) = ab + ac$

or if the multiplication is on the right

$(b + c)a = ba + ca.$

I am going to illustrate with an expression similar to yours, $(2x - 7)(3x + 5).$

The first step is to see $(2x - 7)$ as $a$ in the first form of the distributive law so the expression is $a(3x + 5)$ where $a = (2x - 7).$ Thus

1. $(2x - 7)(3x + 5) = (2x - 7)(3x) + (2x - 7)(5)$

Now you have two instances of the second form of the distributive law, the first with $a = 3x$ and the second with $a = -7.$ Thus step 2 is

1. $(2x - 7)(3x) + (2x - 7)(5) = (2x)(3x) + (-7)(3x) + (2x)(5) + (-7)(5).$

Step 3 is to simplify and collect like terms to get

1. $6x^2 - 21x + 10x -35 = 6x^2 - 11x - 35.$

With a little practice you can skip step 2 and go directly from step 1 to step 3. With a little more practice you will be able to go from the original problem directly to step 3.

Now try your problem,
Penny      Math Central is supported by the University of Regina and the Imperial Oil Foundation.