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.

$=> 60 + 14 = 74$

How do you rewrite 2 \times 372 \times 37 as the sum of two products?