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Polynomial

See how to simplify a polynomial.
18 examples and their solutions.

Adding and Subtracting the Terms of a Polynomial

Example

7x2 - 3x + 2x2 + 8x
Solution

Example

3a2 + 2ab + ab2 - 6ab + 9ab2 - a2
Solution

Multiplying a Monomial and a Polynomial

Example

x(3x2 - 5x + 8)
Solution

Example

(5 - a + 3b)a - 3(a2 + ab - 2)
Solution

FOIL Method: Multiplying Two Binomials

Example

(x - 2)(x - 3)
Solution

Multiplying Polynomials

Example

(x - 3)(x2 - x + 7)
Solution

Example

(x2 + 7x - 1)(3x2 - x + 8)
Solution

(a + b)2

Formula

(a + b)2
= a2 + 2ab + b2

Example

(x + 3)2
Solution

(a - b)2

Formula

(a - b)2
= a2 - 2ab + b2

Example

(x - 7)2
Solution

(a + b)(a - b)

Formula

(a + b)(a - b)
= a2 - b2

Example

(x + 2)(x - 2)
Solution

Example

103⋅97

(Use the above formula.)
Solution

Example

(x2 + 1)(x + 1)(x - 1)
Solution

(a + b)3

Formula

(a + b)3
= a3 + 3a2b + 3ab2 + b3

Example

(x + 2)3
Solution

(a - b)3

Formula

(a - b)3
= a3 - 3a2b + 3ab2 - b3

Example

(x - 5)3
Solution

Dividing a Polynomial by a Monomial

Example

5x2 - 3xx
Solution

Example

12x2y + 4xy32xy
Solution

Example

6x5 + 3x4 - 12x23x2
Solution

Long Division

Example

x2 + 3x - 10x - 2

(Use the long division.)
Solution