The method used to solve this problem can be referred to as the FOIL Method, this is an acronym that stands for First, Outer, Inner, Last. The acronym lets the learner solve the equation by following the letters, multiply First term in each bracket, multiply the Outer two terms in each bracket, multiply the Inner two terms in each bracket and finally the Last two terms in each bracket. This method ensures all relevant terms are calculated.
Expansion Step
First term in each set of brackets are x in this problem,Multiply the first x by the second x to get x² as (xx)=x²This is the first term in our expansion.
Outer term in each set of brackets are x in the first bracket and -8 in the second. It is important to notice this is -8, not simply 8. Using 8 would lead to an incorrect solution.Multiplying x and -8, gives x-8=-8x - Do not forget to keep the minus sign!
Inner two terms are 6 in the first bracket and x in the second. Multiplying the 6 and the x gives 6x=6x - giving our third term.
Last two terms in each of the brackets are 6 and -8These can be multiplied to get -48.
Collect all the terms we have got to give :x²-8x+6x-48
Simplification step By looking at our above solution we can see that as there is a -8x and a +6x, as these are both containing an x term, these can be summed to get -2x, as -8+6 is -2. It is important to note that x² cannot be summed with these as it stands for (xx).
This provides a final solution ofx²-2x-48

4x+2y=22, (y/2)+(x/4)=2.5

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