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Prove that the difference between the squares of any two consecutive integers is equal to the sum of these two integers.

A problem of this nature seems complex at first until you break it down and see what it is really asking you to find. We can represent two consecutive integers as x and x + 1. The problem asks us to prove...

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Simplify 3 × a × 3 × a

The question asks you to simplify an expression, this means we need to write it with as few symbols and numbers as we can.Multiplication is commutative, this means that it doesn't matter which order we do...

Answered by Rob G. • Maths tutor

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Simplify 7 × e × f × 8

Always do the numbers first before dealing with the letters. We move the numbers to one side, and the letters to the other. (7 x 8) x e x f -> I have enclosed the

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Solve the simultaneous equations x^2 +8y=20 and y=x+4

To begin you must substitute the value of y provided into the first equation. The would change the equation into the following form:x^2+8(x+4)=20. Now expand the bracket so that the equation becomes:x^2+8...

Answered by Anthony M. • Maths tutor

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Solve the following simultaneous equations. x^2 + 2y = 9, y = x + 3

x^2 + 2y = 9y = x + 3
x^2 + 2y = 9x^2 + 2(x+3) = 9x^2 + 2x + 6 = 9x^2 + 2x - 3 = 0(x + 3)(x - 1) = 0x= -3, x = 1
when x = -3y = x + 3y = (-3) + 3y = 0
when x = 1y = x + 3y = (1) + 3y = 4

Answered by John F. • Maths tutor

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