How do you simplify $7 a^{2} - 2 a^{2}$ $7a^2 - 2a^2$ ?

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How do you simplify $7 a^{2} - 2 a^{2}$ $7a^2 - 2a^2$ ?

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Answer 1 · 2015-11-03T12:04:19

$7 a^{2} - 2 a^{2} = 5 a^{2}$ $7a^2-2a^2 = 5a^2$

Explanation:

Suppose you have square sheets of material; each sheet is identical to every other sheet and each sheet has dots arranged in a rectangular grid of $a$ $a$ rows and $a$ $a$ columns. There are $a \times a = a^{2}$ $axxa =a^2$ dots on each sheet of material.

Suppose you start the day with $7$ $7$ such sheets of material; you start with $7 \times a^{2}$ $7xxa^2$ or more simply $7 a^{2}$ $7a^2$ dots.

If during the day you lose $2$ $2$ of those sheets of material, you will have lost $2 \times a^{2}$ $2xxa^2$ or $2 a^{2}$ $2a^2$ dots.

During the day, $7$ $7$ sheets minus $2$ $2$ sheets becomes $5$ $5$ sheets
$XXX 7 sheets - 2 sheets = 5 sheets$ $color(white)("XXX")7" sheets" - 2" sheets" = 5" sheets"$
and $7 \times a^{2}$ $7xxa^2$ dots minus $2 \times a^{2}$ $2xxa^2$ dots becomes $5 \times a^{2}$ $5xxa^2$ dots
$XXX 7 a^{2} - 2 a^{2} = 5 a^{2}$ $color(white)("XXX")7a^2-2a^2=5a^2$

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How do you simplify $7 a^{2} - 2 a^{2}$ $7a^2 - 2a^2$ ?

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