SEARCH HOME
Math CentralQuandaries & Queries

search

Question from symion, a student:

expand and simplify [x-3][x+3]

Ho Symion,

For this problem I would use the distributive property which says that

\[a (b + c) = a b + a c\]

or written with the multiplication on the right

\[(d + e) f = d f + e f.\]

I am going to illustrate with two problems similar to yours.

Expand and simplify $(x - 3) (x + 2).$

To apply the distributive law think of $(x - 3)$ as $a$ and you get

\[(x - 3) (x + 2) = (x - 3) \times x + (x - 3) \times 2.\]

Now apply the distributive law with the multiplication on the right to get

\[(x - 3) \times x + (x - 3) \times 2 = x \times x + (-3) \times x + x \times 2 + (-3) \times 2.\]

Collecting like terms results in

\[(x - 3)(x + 2) = x^2 -x -6.\]

For a second example

expand and simplify $(x + 5) (x + 5).$

Using the same technique I uses for the first example

\[(x + 5) (x + 5) = (x + 5) \times x + (x + 5) \times 5 = x \times x + 5 \times x + x \times 5 + 5 \times 5\]

which simplifies to

\[(x + 5)(x + 5) = x^2 + 10 x + 25.\]

Now try your problem,
Penny

About Math Central
 

 


Math Central is supported by the University of Regina and the Imperial Oil Foundation.
Quandaries & Queries page Home page University of Regina