Exponents and Polynomials

Adding and Subtracting Polynomials

Add polynomials by combining like terms: match terms with the same degree and add their coefficients. x^2 terms combine with x^2 terms, x terms with x terms, and constants with constants.

add-subtract-polynomials Group by degree, then add coefficients. The degree structure of the result matches the highest degree present in either polynomial.

Example

Combine like terms and distribute a minus sign before subtracting.

highlighted = computed this step

Step 1 — Add setup

Set up the expression.

3x2+2x+1+(2x2+4x+2)3x^{2} + 2x + 1 +( 2x^{2} + 4x + 2 )

Step 2 — Combine squared terms

Combine coefficients: 3 + 2 = 5.

3+2=53 + 2 = \hl{5}

Step 3 — Combine x terms

Combine coefficients: 2 + 4 = 6.

2+4=62 + 4 = \hl{6}

Step 4 — Combine constants

Combine coefficients: 1 + 2 = 3.

1+2=31 + 2 = \hl{3}

Step 5 — Addition result

Read the final result.

5x2+6x+35x^{2} + 6x + 3

Step 6 — Distribute minus

Distribute the minus: 2, 4, 2 become -2, -4, -2.

−(2x2+4x+2)=−2x2−4x−2-( 2x^{2} + 4x + 2 )=- \hlmath{2x^{2}} - \hlmath{4x} - \hl{2}

Step 7 — Subtract coefficients

Subtract coefficients: 3 - 2 = 1, 2 - 4 = -2, 1 - 2 = -1.

3−2=12−4=-21−2=-13 - 2 = \hl{1} \quad 2 - 4 = \hl{-2} \quad 1 - 2 = \hl{-1}

Step 8 — Subtraction result

Read the final result.

x2−2x−1x^{2} - 2x - 1