Oxford PAT 2014, Question 4

2014_page4

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5 thoughts on “Oxford PAT 2014, Question 4

  1. Could you please explain your working to this question to me please? :/ I’m confused at the second line, and the last one.

    1. The second line is : ((1+2x)^4)((1-2x)^6) = (((1+2x)(1-2x))^4)(1-2x)^2

      We know that a^(m+n) = (a^m)(a^n), so ((1-2x)^6) can be rewritten as ((1-2x)^4)((1-2x)^2). We also know that (a^n)(b^n)c = ((ab)^n)c, so we can rewrite ((1+2x)^4)((1-2x)^4)((1-2x)^2) as ((1+2x)(1-2x)^4)((1-2x)^2).

      When we look at the second-last line we see we can only get x^7 by multiplying the term -4(4x^2)^3 by the term -4x. So the coefficient of x^7 is 4 x 4 x 4^3 which is 4^5. We know that 4^5 = 2^10, which is 1024.

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