Question

How do you use the distributive law to multiply `12 xx 12` ?

Answer 1

See explanation...

Explanation:

Multiplication is distributive over addition. That is:

For any numbers `a`, `b` and `c`:

`a(b+c) = ab+ac" "` (left distributive)

`(a+b)c = ac+bc" "` (right distributive)

So we can split the multiplication of `12 xx 12` down like this:

`12 xx 12 = 12(10+2) = (12 xx 10) + (12 xx 2) = 120+24 = 144`

In fact, we are using this distributive property when we use long multiplication:

`color(white)(0+0)12color(lightgray)0" "larr 12xx1color(grey)(xx10)`
`color(white)(0)+color(white)(0)underline(color(white)(0)24)" "larr 12xx2color(grey)(xx1)`
`color(white)(0+0)144`

`color(white)()`

If you are only comfortable with multiplying numbers up to `10xx10` then we could split it down even further, like this:

`12 xx 12 = 12(10+2)`

`color(white)(12 xx 12) = (12 xx 10) + (12 xx 2)`

`color(white)(12 xx 12) = ((10+2) xx 10) + ((10+2) xx 2)`

`color(white)(12 xx 12) = ((10xx10)+(2xx10)) + ((10xx2)+(2xx2))`

`color(white)(12 xx 12) = (100+20) + (20+4)`

`color(white)(12 xx 12) = 100+(20+20)+4`

`color(white)(12 xx 12) = 100+40+4`

`color(white)(12 xx 12) = 144`