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Subtract polynomials

Subtracting polynomials is understood as adding the additive inverse of the subtrahend: every term in the polynomial being subtracted changes sign, and only like terms—those with identical variable parts and exponents—are combined by adding their coefficients. This includes simplifying one-variable polynomials with integer or rational coefficients and whole-number exponents, supporting later work with equations and functions; polynomial division, multivariable generalizations, and abstract polynomial theory are outside this scope.

Detailed Explanation: Subtract polynomials

To subtract polynomials, change the sign of every term in the polynomial being subtracted. Then combine like terms.

Example:

(3x25x+7)(x2+2x4)(3x^2-5x+7)-(x^2+2x-4)

Step 1: Change the signs in the second polynomial.

The subtraction sign applies to every term:

3x25x+7x22x+43x^2-5x+7-x^2-2x+4

Step 2: Group like terms.

Like terms have the same variable and exponent:

(3x2x2)+(5x2x)+(7+4)(3x^2-x^2)+(-5x-2x)+(7+4)

Step 3: Combine the coefficients.

2x27x+112x^2-7x+11

Therefore,

(3x25x+7)(x2+2x4)=2x27x+11\boxed{(3x^2-5x+7)-(x^2+2x-4)=2x^2-7x+11}

Remember: only combine like terms, such as x2x^2 with x2x^2 and xx with xx.

Learn by doing: Subtract polynomials

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Like Terms - Combine - Order 2 - Fractional - One Variable - Expression to Pair


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