# #\$ Add and Subtract Polynomials

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## How to Add and Subtract Polynomials

1. Identify the “invisible” coefficients of 1.
2. Distribute the coefficients outside of the parentheses to all the terms inside parentheses.
3. Combine like terms.

$(3x^4-2x^3+7x-1)+(x^3-6x^2+8x-5)$

What are the “invisible” coefficients outside the parentheses that need to be distributed to the terms inside?

The first polynomial has an invisible coefficient of +1 outside the parentheses. The second polynomial also has a +1 coefficient because we are adding the second polynomial to the first.

${\green+1}(3x^4-2x^3+7x-1){\purple +1}(x^3-6x^2+8x-5)$

When I multiply the terms inside the parentheses by +1, all of the coefficients stay the same.

${\green +3}x^4{\green -2}x^3{\green+7}x{\green -1}{\purple +1}x^3{\purple -6}x^2{\purple +8}x{\purple -5}$

Are there any like terms?

Yes, there are two $$\red -x^3$$ terms, two $$\yellow x$$ terms, and two constant terms.

$3x^4{\red -2x^3}{\yellow +7x}{\blue -1}{\red +1x^3}-6x^2{\yellow +8x}{\blue -5}$

When I combine these like terms, the simplified expression is…

$3x^4{\red -1x^3}-6x^2{\yellow +15x}{\blue -6}$

The sum of $$3x^4-2x^3+7x-1$$ and $$x^3-6x^2+8x-5$$ is…

$3x^4-x^3-6x^2+15x-6$