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Prove that the difference between the squares of two consecutive odd numbers is a multiple of 8.

(2n+3)²-(2n+1)²=(4n²+12n+9)-(4n²+4n+1)=8n+8= 8(n+1)Hence a multiple of 8

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Prove that the square of an odd number is always 1 more than a multiple of 4

2n+1 will always be an odd number (e.g. if n is equal to 3 the answer would be 7, an odd number) So, we square 2n+1 and write this as (2n+1)² 2n +12n 4n...

Answered by • Maths tutor

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There are 495 coins in a bottle. 1/3 of the coins are £1 coins. 124 of the coins are 50p coins. The rest of the coins are 20p coins. Work out the total value of the 495 coins

495/3 = 165 => £165 worth of £1 coins
124 x 0.5 = 62 => £62 worth of 50p coins
We know the number of coins that are NOT 20p coins. Therefore, we can subt...

Answered by Sim B. • Maths tutor

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25* 3/2

25^3/2= 25^{(3x 1/2)}(25^1/2)³= (square root of 25)³(5)³= 125

Answered by Aisha B. • Maths tutor

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Prove algebraically that the straight line with equation x = 2y + 5 is a tangent to the circle with equation x^(2) + y^(2) = 5

If a line is a tangent to a circle, it will have exactly one point where the line intersects the circle. Therefore, when we set the equation of the straight line equal to the equation of the circle, we sh...

Answered by Rawdah H. • Maths tutor

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