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Solve: 6x + 3 = 3x + 9

There are a few ways to tackle this particular style of problem. First off we can try doing it without using any bracket theory and just focus on the raw numbers (a somewhat simpler approach). Step 1: We're ...
CG
Answered by Calum G. • Maths tutor
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prove that (3x+1)^2 - (3x-1)^2 is a multiple of 4 for all positive integer values of x

(3x + 1) 2 = 9x 2 + 6x + 1 (3x - 1) 2 = 9x 2 - 6x + 1 (9x 2 + 6x + 1) - (9x 2 - 6x + 1) = 12x 12x/4 = 3x Therefore for all positive integers of x the result is a multiple of 4
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Answered by Katie J. • Maths tutor
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Differentiate the following function u = Cos(x3)

u = Cos(x 3 ) To differentiate this function we will use the chain rule. Firstly we will set x 3 to another variable name such as v. So now v = x 3 . Lets differentiate this. dv/dx = 3x 2 We can now differen...
SB
Answered by Serena B. • Maths tutor
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Prove that the sqrt(2) is irrational

To do this we will assume sqrt(2) is rational , a fraction, which means: 2 1/2 = m/n ; m,n belong to integers. Also, m/n is an irreductible fraction , meaning m and n have no common divisors. 2 1/2 = m/n &lt...
JC
Answered by Joao C. • Maths tutor
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Expand and simplify 2(a + 3) + 5(a – 1)

Firstly we will start by expanding the brackets. We will do 2 a + 2 3 for the first bracket, then we will do 5 a + 5 (-1) for the second bracket which will give us 2a + 6 + 5a - 5. We will then simplify what...
SB
Answered by Serena B. • Maths tutor
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