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 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

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