We are currently working on a unit of algebra.
We have already looked at expanding brackets. This involves multiplying either a number through a set of brackets, or multiplying a full bracket trough using the FOIL technique. FOIL stands for Firsts, Outers, Inners, Lasts, and it helps us to remember the order for multiplying two brackets with one another. For example:
For more information on this, see: http://www.mathsisfun.com/algebra/expanding.html
We also have to remember to collect like terms. This means adding or subtracting the terms which are the same as other terms. For terms to be "like terms" they must have exactly the same combination of pronumerals (letters). For example, 2x and 2xy are not like terms, because one has an x, however the other has an x and a y. 4a and 26a are like terms, because they both only have an a and no other pronumerals.
For more information on this, see: http://www.mathsisfun.com/algebra/like-terms.html
We are now looking at factorising. This involves taking out the highest common factor from the terms in an expression, and then writing the rest of the expression in brackets. A factor of a number is another number that goes into (or divides) this number. For example, 8 has the factors of 1, 8, 2, and 4.
Common factors are factors that two numbers share. For example, 8 has the factors 1, 8, 2, and 4, and 12 has the factors 1, 12, 2, 6, 3, and 4. This means that the common factors of 12 and 8 are 1, 2, and 4.
The highest common factor is the common factor that contains the most "stuff". This means it has the highest number, as well as the most pronumerals (letters). If we look at the factors of 8 and 12 again, the highest common factor is 4.
Finally, if we are asked to factorise an expression, the first step is to find the highest common factor.
For example: Factorise 4x + 8
The factors of 4x are: 1, 4x, 4, x, 2, 2x
The factors of 8 are: 1, 8, 2, 4
So the highest common factor is 4.
We now have to take this out the front of the brackets, and put the rest of the stuff in the brackets.
So we have: 4(? + #)
To work out what ? is: "What do we multiply 4 (our highest common factor out the front) by to get 4x?" The answer to this is x, so our ? is x.
To work out what # is: "What do we multiply 4 (our highest common factor out the front) by to get 8?" The answer to this is 2, so our # is 2.
So finally, we get: 4(x + 2) as our final answer when we are asked to factorise 4x + 8
For more examples, see https://www.mathsisfun.com/algebra/factoring.html
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