How do you rewrite #2 \times 37# as the sum of two products?

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Answer 1 · 2018-07-06T13:44:19

Set 37 as 100-63 giving: #2xx37->2xx(100-63)#

#[200]+[-126] #

#2xx(37) = 74#

'Split' the 37 (partition it) into the sum of any two numbers.

Just to be different I select such that one of them is negative.

Set #37=color(red)(100 - 63)# so we have:

#color(green)(2xx(color(red)(37)) color(white)("d")-> color(white)("d")2xx(color(red)(100-63)) )#

Multiply everything inside the brackets by the 2 that is outside.

#color(green)([2xxcolor(red)(100)] +[2xx(color(red)(-63))] )#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Check")#

#[200]-[126] = 74 larr" As required"#

Answer 2 · 2018-07-06T13:47:01

#color(brown)(=> 2 * 30 + 2 * 7#

#2 * 37 = (2* (30 + 7))# Distributive Law

#=> 2 * 30 + 2 * 7#

We can write many such sum of two products.

#=> 60 + 14 = 74#