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Calculate the binomial expansion of (2x+6)^5 up to x^3 where x is decreasing.

In order to use the binomial expansion, we must have an 'x' with no coefficients - so no number before it. So we take out a factor of 2:(2(x+3))^5 We can then simplify to:32(x+3)^5 by expanding out 2^5. Now ...
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Answered by Sophie C. • Maths tutor
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Find a solution for the following simultaneous equations: 2x+y=5 and 2x-5y=2

Subtract the 2nd equation from the first: 2x--2x+y+6y=5-2 <=> 7y=3 <=> y=3/7Input the value of y into one of the equations: 2x+3/7=5 <=> 2x=(35-3)/7 <=> x=16/7
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Answered by Darshil C. • Maths tutor
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How would you differentiate a function such as 4x^3

The general rule for differentiating functions such as 4x^3 is called the power rule.This formula goes by dy/dx of [x^n] = nx^(n-1)Now this may seem complicated but with examples hopefully it should become m...
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Answered by Adam W. • Maths tutor
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What is differentiation

Differentiation is a mathematical operation which we can use to study how one quantity, such as the distance travelled by a train, is affected by another quantity, such as time. For example, if the train is ...
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Answered by Oliver B. • Maths tutor
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How do you factorise?

Factorising basically means put whatever equation you are given into brackets. So, E.g. x 2 + xFirst you want to look for a common factor which here is X. Therefore, the answer would be x(x+1).To check this ...
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Answered by Lydia D. • Maths tutor
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