Question

How do you simplify `7a^2 - 2a^2`?

Answer 1

`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` rows and `a` columns. There are `axxa =a^2` dots on each sheet of material.

Suppose you start the day with `7` such sheets of material; you start with `7xxa^2` or more simply `7a^2` dots.

If during the day you lose `2` of those sheets of material, you will have lost `2xxa^2` or `2a^2` dots.

During the day, `7` sheets minus `2` sheets becomes `5` sheets
`color(white)("XXX")7" sheets" - 2" sheets" = 5" sheets"`
and `7xxa^2` dots minus `2xxa^2` dots becomes `5xxa^2` dots
`color(white)("XXX")7a^2-2a^2=5a^2`