Question

Expand and simplify (x+2) (x+3) (x+4)

Answer 1

x^3 + 9x^2 + 26x + 24

Explanation:

Lets break this up into steps. Set brackets and do the opeartion within the brackets, in steps.

(x+2)(x+3)(x+4)

[(x+2)(x+3)](x+4)

[x^2 + 5x + 6](x+4)

(x+4)[x^2 + 5x + 6] I moved the (x+4) term in front for personal preference. This is telling us that we need to multiply [x^2 + 5x + 6] first by x and then by 4, and add the tworesults.

x(x^2 + 5x + 6)+4(x^2 + 5x + 6) Let E = (x^2 + 5x + 6)

x(E)+4(E)

(x^3 + 5x^2 + 6x) + (4x^2 + 20x + 24)

x^3 + 9x^2 + 26x + 24 Combine like terms

Answer 2

`x^3+9x^2+26x+24`

Explanation:

First, distribute many times. Note that I used brackets to clarify what is about to be distributed in the next step.

`(x+2) (x+3) (x+4)`

`= (x+2) \cdot \left[\frac{}{}(x+3)(x+4)\frac{}{}\right]`

`= x(x+3)(x+4)+2(x+3)(x+4)`

`= x(x+3)\cdot \left[ \frac{}{} x+4 \frac{}{}\right]+2(x+3)\cdot \left[\frac{}{}x+4\frac{}{}\right]`

`= x(x(x+4)+3(x+4))+2(x(x+4)+3(x+4))`

`= x\left(x \cdot\left[ \frac{}{}x+4\frac{}{}\right]+3\cdot\left[ \frac{}{}x+4\frac{}{}\right]\right)+2\left(x\cdot\left[ \frac{}{}x+4\frac{}{}\right]+3\cdot\left[ \frac{}{}x+4\frac{}{}\right] \right)`

`= x(x^2+4x+3x+12)+2(x^2+4x+3x+12)`

`= (x^3+4x^2+3x^2+12x)+(2x^2+8x+6x+24)`

Then, combine like terms.

`= x^3+(4x^2+3x^2+2x^2)+(12x+8x+6x)+24`

`= x^3+9x^2+26x+24`