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

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Answer 1 · 2018-07-06T13:44:19

Set 37 as 100-63 giving: $2 \times 37 \to 2 \times (100 - 63)$ $2xx37->2xx(100-63)$

$[200] + [- 126]$ $[200]+[-126]$

$2 \times (37) = 74$ $2xx(37) = 74$

'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 $37 = 100 - 63$ $37=color(red)(100 - 63)$ so we have:

$2 \times (37) d \to d 2 \times (100 - 63)$ $color(green)(2xx(color(red)(37)) color(white)("d")-> color(white)("d")2xx(color(red)(100-63)) )$

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

$[2 \times 100] + [2 \times (- 63)]$ $color(green)([2xxcolor(red)(100)] +[2xx(color(red)(-63))] )$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Check$ $color(blue)("Check")$

$[200] - [126] = 74 \leftarrow As required$ $[200]-[126] = 74 larr" As required"$

Answer 2 · 2018-07-06T13:47:01

$\Rightarrow 2 \cdot 30 + 2 \cdot 7$ $color(brown)(=> 2 * 30 + 2 * 7$

$2 \cdot 37 = (2 \cdot (30 + 7))$ $2 * 37 = (2* (30 + 7))$ Distributive Law

$\Rightarrow 2 \cdot 30 + 2 \cdot 7$ $=> 2 * 30 + 2 * 7$

We can write many such sum of two products.

$\Rightarrow 60 + 14 = 74$ $=> 60 + 14 = 74$

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