Special Products:

(x + y)² = x² + 2xy + y²

(x – y)² = x² – 2xy – y²

(x + y)³ = x³ + 3x²y + 3xy² + y³

(x – y)³ = x³ – 3x²y + 3xy² – y³

You may find looking up Pascal’s Triangle to be useful for multiplying out quantities raised to larger powers. For example (x + y)⁶.

Pascal’s Triangle:

1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

From the above you should be able to discover

(x + y)⁶ = x⁶ + 6x⁵y + 15x⁴y² + 20x³y³ + 15x²y⁴ + 6xy⁵ + y⁶

Notice the coefficients correspond to the numbers in the sixth row of Pascal’s triangle.