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Binomial Expansion

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Question 40

The binomial expansion of (3+2x)4(3 + 2x)^4(3+2x)4 is given by

(3+2x)4=A+Bx+216x2+Dx3+16x4 (3 + 2x)^4 = A + Bx + 216x^2 + Dx^3 + 16x^4 (3+2x)4=A+Bx+216x2+Dx3+16x4
a.

Find the value of AAA and the value of BBB.

[3]
b.

Show that

(3+2x)4−(3−2x)4=Cx+Dx3 (3 + 2x)^4 - (3 - 2x)^4 = Cx + Dx^3 (3+2x)4−(3−2x)4=Cx+Dx3

where CCC and DDD are constants to be found.

[4]
c.

Hence, or otherwise, find

∫((3+2x)4−(3−2x)4)dx \int \left( (3 + 2x)^4 - (3 - 2x)^4 \right) dx ∫((3+2x)4−(3−2x)4)dx
[3]

Binomial Expansion Questions

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