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Can you please explain how to expand two brackets, eg. (3x-7)(5x+6)

When I am expanding brackets I use the acronym FOIL and simplify. You begin by multiply the first term (F) in each bracket, followed by multiplying the outside terms (O), then the inside terms (I) and finall...
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Given that cos(x) = 1/4, what is cos(2x)?

cos(2x) = 2cos 2 (x) - 1 This is the identity. Therefore we can substitute in 2[cos 2 (x)] to be 2 multiplied by (1/4) 2 .Therefore cos(2x) = 2(1/4)(1/4) - 1 = 2/16 - 1 = 2/16 - 16/16 =1/8 - 8/8 = -(7/8).Ans...
BK
Answered by Bhumi K. • Maths tutor
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Expand (2x+4)(x-3)

2x^2 - 2x - 12
AS
Answered by Amy S. • Maths tutor
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n is an integer such that 3n + 2 < 14 and 6n/(n^2+5) > 1. Find all possible values of n.

First of all, solving the equation 3n + 2 &lt; 14 to find n. 3n &lt; 14 -2 = 3n &lt; 12. n &lt; 12/3 = n &lt; 4Secondly solve the equation 6n/(n^2+5) &gt; 1 to find n. Collect all terms on one side of the to...
KP
Answered by Kai P. • Maths tutor
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Split (3x-4)/(x+2)(x-3) into partial fractions

(3x-4)/(x+2)(x-3) = A/(x+2) + B/(x-3)=&gt; 3x-4 = A(x-3) + B(x+2)Let x = -2-10 = -5AA = 2Let x = 35 = 5BB = 1∴ (3x-4)/(x+2)(x-3) = 2/(x+2) + 1/(x-3)
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