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 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.