Question

8. Expand (1 + 2x + 3x^2) in a series of ascending powers of x up to and including the term in x^2.

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Answer 1

Answer:

Pascal’s Triangle

You should know that (a + b)² = a² + 2ab + b² and you should be able to work out that (a + b)³ = a³ + 3a²b + 3b²a + b³ .

It should also be obvious to you that (a + b)¹ = a + b .

so (a + b)¹ = a + b

(a + b)² = a² + 2ab + b²

(a + b)³ = a³ + 3a²b + 3b²a + b³

You should notice that the coefficients of (the numbers before) a and b are:

1 1

1 2 1

1 3 3 1

If you continued expanding the brackets for higher powers, you would find that the sequence continues:

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

etc