# Thread: Distributive Law of Multiplication Using Variables

1. ## Distributive Law of Multiplication Using Variables

I'm having some trouble with this concept. Expression:

3x(4x + 5)

and another one

-2x(3x - 12)

2. Recall $\displaystyle a(b+c) = a\times b +a\times c$

Therefore

$\displaystyle 2x(7x+4) = 2x\times 7x+2x\times 4 = 14x^2+8x$

and

$\displaystyle -12x(6x-3) = -12x\times 6x-12x\times -3 = -72x^2+36x$

Use these examples to do yours.

3. $\displaystyle 3x(4x + 5)$
$\displaystyle 3x(4x) + 3x(5)$
$\displaystyle 12x^2 + 15x$

$\displaystyle -2x(3x - 12)$
$\displaystyle -2x(3x) -2x(-12)$
$\displaystyle -6x^2 + 24x$

4. Thanks. I have another question, what's 14x^2 + x^2?

Is that 15x^2?

5. And 2x(x + 3) = 3x + 3? Or 2x^2 + 3?

6. Originally Posted by ahhlecks
Thanks. I have another question, what's 14x^2 + x^2?

Is that 15x^2?
Yep

7. Originally Posted by ahhlecks
And 2x(x + 3) = 3x + 3? Or 2x^2 + 3?
Neither, $\displaystyle 2x(x + 3) = 2x^2 + 6x$

8. Thank you.

This one's got me stumped.

4x^2(5x + 6) + 2x(x^2 + 10x - 12)

9. I got

20x^3 + 24x^2 + 4x^3 + 20x^2 - 24x

= 24x^3 + 44x^2 - 24x