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Expand and Simplify: 16=(x-3)(x+3)

16 = (x-3)(x+3) --> 16 = x^2+3x-3x-9 --> 16 = x^2-9 --> x^2=25 --> x = +5 or -5
TT
Answered by Thaarabi T. • Maths tutor
4668 Views

Prove algebraically that (4n + 1)² − (2n − 1) is an even number for all positive integer values of n.

First of all expand the brackets and simplify the expression given:(4n+1)(4n+1)-(2n-1)= 8n 2 +8n+1-2n+1= 8n 2 +6n+2= 2(4n 2 +3n+1). Since the expression can be factorised with 2, and since 4n 2 +3n+1 will al...
SM
Answered by Shiv M. • Maths tutor
11596 Views

If a particle of mass m is launched vertically upwards from the ground with velocity u m/s, how long will it take to return to the ground in terms of m, u and g?

Taking upwards to be positive, and using the 'suvat' equation s=ut+1/2at 2 we know that u=u, a=-g and s=0 when the particle returns to the ground. Then we solve for t: 0=ut-1/2gt 2 0=t(u-1/2gt) So the partic...
JV
Answered by Jackie V. • Maths tutor
3688 Views

How to recognise and make the link between probability and the algebraic demands of this question?

While I doubt students will ask this exact question, think it provides the basis for what are usually the most difficult questions in GCSE papers, and students would usually be unsure where to start. My insp...
NK
Answered by Neeraj K. • Maths tutor
3423 Views

Use the substitution u=x^2-2 to find the integral of (6x^3+4x)/sqrt( x^2-2)

First use the substitution to find du/dx which is 2x. From this we now know that dx= du/2x (just re-arranging.) Substituting that into the integral we now get (6x 3 +4x)/ (sqrt (u) x 2x) du. Cancelling out t...
KS
Answered by Khalil S. • Maths tutor
10788 Views