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

1 Answer
Jan 6, 2017

Answer:

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#