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Binomial Expansion

Binomial Expansion

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Question 333

A model for the energy output, E(x)E(x)E(x), of a specialized transducer under mechanical stress is defined by the function E(x)=(3+4x)4E(x) = (3 + 4x)^4E(x)=(3+4x)4, where xxx is the applied strain. The expansion of this function is given by

(3+4x)4=A+Bx+864x2+768x3+256x4 (3 + 4x)^4 = A + Bx + 864x^2 + 768x^3 + 256x^4 (3+4x)4=A+Bx+864x2+768x3+256x4
a.

Find the values of the constants AAA and BBB.

[2]
b.

Show that

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

where CCC and DDD are constants to be found.

[3]
c.

Hence, or otherwise, find

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

Binomial Expansion Questions

  1. A Level
  2. /Maths
  3. /Binomial Expansion

409 exam-style questions on Edexcel A Level Maths Binomial Expansion, covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions. Each one has a worked solution and a mark scheme showing where the marks go.

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