Multiplying Polynomials Exercises

Multiply x² – 3x + 2 by x – 2.

Hint

Multiply everything out to get x³ – 2x²– 3x² + 6x + 2x – 4, then combine like terms.

Multiply a – 2b – c by a – b + 2c.

Hint

A little distributive property action gets us to a² – ab + 2ac – 2ab + 2b² – 4bc – ac + bc – 2c².

Multiply m² + mn + n² by m² – mn – n².

Hint

Rewrite as m⁴ – m³n – m²n² + m³n – m²n² – mn³ + m²n² – mn³ – n⁴, then lump all the like terms together.

Multiply (x – 3)(2x² – 3x – 2).

Hint

Distribute to get 2x³ – 3x² – 2x – 6x² + 9x + 6.

Multiply x⁴ + x² – 1 by x⁴ – x² + 1.

Hint

After distributing, we get x⁸ – x⁶ + x⁴ + x⁶ – x⁴ + x² – x⁴ + x² – 1. The rest is up to you.

Multiply (a²b² + a²b²)(a² – 2ab + b²).

Hint

Rewrite as a⁴b² – 2a³b³ + a²b⁴ + a⁴b² – 2a³b³ + a²b⁴.

Multiply and .

Hint

Remember that when terms with exponents are multiplied together, we add the exponents.