Expand in terms of ascending powers of x

Use Pascal's Δ 1

1 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

(a + b)^{6} = a^{6} + 6a^{5}b + 15a^{4}b^{2} + 20a^{3}b^{3} + 15a^{2}b^{4} + 6ab^{5} + b^{6}

1. If you notice, that coefficients are from the bottom of Pascal 's triangle.

2. The powers of **a** go down, from 6 to 0;

3. The exponents of **b** go up, from 0 to 6;

4. The sum of the powers of each therm equal 6;

5. If you multiply all coefficients you will get 2^{6} = 64 (for each row of Pascal's Δ 2^{n})

Now replace a by 7 and b by (-4x)

7^{6} - 6 · 7^{5} · 4x + 15 · 7^{4} · (-4x)^{2} - 20 · 7^{3} · (4x)^{3} + 15 · 7^{2} · (-4x)^{4} - 6 · 7 · (4x)^{5} + (-4x)^{6}

## Comments

There were two answers from yesterday that were not posted when I posted my response. Had they been present I would not have replicated their efforts. The tedious nature of Wyzant withtheir sluggish responses caused this duplicity.

George- I feel the same way, sometimes I will submit an answer and it comes up instantly and sometimes it takes days. Very frustrating.