How to Combine Like Terms With Polynomials

Polynomial equations can be overwhelming at first, but they need not be. From a sea of exponents and parentheses, like terms--those terms in an equation with identical variables--can be combined to make even the most awkward equations far more manageable.

Instructions

Difficulty: Easy

1. Work through your parentheses. For example, 25 – 2[(12x² – 7) – (4x² – 5)]+(3x + 2)² would be simplified to 25 – 2(12x² – 7 – 4x² + 5)+(3x+2)². You can simplify further within the parentheses to 25 – 2(8x² – 2)+(3x+2)².
2. Calculate the exponents: 25 – 2(8x² – 2)+(3x+2)² would become 25 – 2(8x² – 2)+(9x²+12x+4) Make sure that you include operations like (x)(x), which becomes x², and not 2x.
3. Multiply and divide. Now, 25 – 2(8x² – 2)+(9x²+12x+4) would become 25 – 16x² + 4+9x²+12x+4.
4. Finally, add and subtract your like terms--terms with identical variables, like x² or x. The final product would become -7x² + 12x + 33.
5. Double-check your work.

Tips & Warnings

• Steps 1 through 4 form the acronym PEDMAS, for Parentheses, Exponents, Divide and Multiplication, Addition and Subtraction. This is the "order of operations" for equations.
• Don't add different variables, even if they are of the same power: 3x + y remains 3x + y.