Question

In rational expressions how do i “expand” terms? example: (x+2)(x-2)(x+3)?

Answer 1

Hello!

I'll show you one way to solve this specific exercise:

First, notice that we have three factors, right?

• 1st factor: (x+2)

,

• 2nd factor: (x-2)

,

• 3rd factor: (x+3)

We have to multiply the first by the second factor, look:

`\begin{gathered} (x+2)\cdot(x-2) \\ (x\cdot x)+\mleft\lbrace x\cdot(-2)\}+(2\cdot x)+\mleft\lbrace2\cdot(-2\mright)\mright\rbrace \\ x^2-2x+2x-4 \\ x^2-4 \end{gathered}`

Multiplying the first by the second factor, we obtained the expression above: x² -4. Now, we'll have to multiply this obtained expression by the third factor, look:

`\begin{gathered} (x^2-4)(x+3) \\ (x^2\cdot x)+(x^2\cdot3)+\mleft\lbrace(-4\mright)\cdot x\}+\mleft\lbrace(-4\mright)\cdot3\} \\ x^3+3x^2-4x-12 \end{gathered}`

According to the reasoning above, the expression (x+2)(x-2)(x+3) is the same as that x³+3x²-4x-12.