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To factorise 3a3b + 12a2b2 + 9a5b3, we need to deal with like elements together.
Start with the integers. The highest common factor of 3, 12, and 9 is 3. Therefore we factor out the 3 and the expression becomes
3(a3b + 4a2b2 + 3a5b3)
Next, deal with the a values. The highest common factor of a3, a2 and a5 is a2. So, we factor out a2and the expression becomes
3a2(ab + 4b2 + 3a3b3)
Finally, we need to factorise the b values. The highest common factor of b, b2 and b3 is b. So we factor out b and the expression becomes.
3a2b(a + 4b + 3a3b2).
Therefore, the complete factorisation of 3a3b + 12a2b2 + 9a5b3 is 3a2b(a + 4b + 3a3b2).see more
To answer this question, we need to form an equation to work out the nth term of the series.
To do this, the first thing we do is calculate the difference between each term.
7 - 3 =4
11 - 7 = 4
15 - 11 = 4
The difference each time is 4. Therefore, the equation could be 4n. Let's try it out with the first term.
4n = 4 x 1 = 4 which is not equal to the first term, 3.
To get 3 from the equation we have at the moment, we need to subtract 1.
Let's try the second term with the equation 4n -1.
4n-1 = 4x2 -1 = 7 which is equal to the second term.
To double check that we're right, let's use the equation to calculate the 5th term.
4n -1 = 4x5 -1 = 19.
19 is 4 greater than 15, so we're right!
Now let's calculate the 100th term.
4n -1 = 4x100 -1 = 399
Therefore the 100th term of this sequence is 399see more
To do this, we first need to calculate the prime factorisations of 432 and 522, that is to say we need to break the numbers down into their prime factors.
Let's start with 432.
432 = 2 x 216
432 = 2 x ( 2 x 108)
432 = 2 x 2 x (2 x 54)
432 = 2 x 2 x 2 x (9x6)
432 = 2 x 2 x 2 x (3 x 3) x (2 x 3)
Therefore, the prime factorisation of 432 is 24 x 33
SImilarly with 522,
522 = 2 x 261
522 = 2 x (3 x 87)
522 = 2 x 3 x (3 x 29)
Since 29 is a prime number, the prime factorisation of 522 is 2 x 32 x 29.
Now, to calculate the highest common factor of the two numbers, we can draw a Venn diagram to find the intersection of the two factorisations.
For now, imagine it like this.
432 BOTH 522
23 3 2 32 29
Therefore, the intersection of the two factorisations is 2 and 32, which means that the highest common factor is just those numbers multiplied.
So the HCF of 432 and 522 = 2 x 32 = 18see more