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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

x(3x2 - 5x + 8)
Solution

### Example

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

(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
= a2 + 2ab + b2

(x + 3)2
Solution

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

(x - 7)2
Solution

## (a + b)(a - b)

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

(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

(x + 2)3
Solution

## (a - b)3

### Formula

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

(x - 5)3
Solution

## Dividing a Polynomial by a Monomial

5x2 - 3xx
Solution

12x2y + 4xy32xy
Solution

### Example

6x5 + 3x4 - 12x23x2
Solution

## Long Division

### Example

x2 + 3x - 10x - 2

(Use the long division.)
Solution