How do you add and simplify #3x^2-4x+7# and #2x^3-4x^2-6x+5#?

1 Answer
Dec 15, 2014

You can add the two expressions and then evaluate the operations involving SIMILAR factors to simplify the expression.
Similar factors are the ones with the same literal forms.
For example: #3x^3,-13x^3,x^3# are similar and you can add or subtract them.
Instead: #3x^2, 14x, -5x^4# are not similar (x appears with different powers) and you can not add or subtract them.
Numbers alone can always be added or subtracted.

In our case we add the two expressions:
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We can underline the similar factors with wiggly lines, dotted lines or arrows.
We can now add together (respecting the signs) similar factors to get:
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Remember that if you were to subtract the two expressions you would have needed to change all the signs of the second expression.