Why is the problem flipped in the last step and is there anything else I need to do or is that it?   (3+7x)(6+2x)

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embizze | High School Teacher | (Level 2) Educator Emeritus

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Your original question was how to multiply two binomials. You had done all of the work and wanted to verify the answer:


In essence, you will use the distributive property of multiplication over addition: first distribute the 3 across (6+2x) and then distribute 7x across the binomial. Sometimes the method is taught as FOIL (first, outside, inside, last.) I do not like this mnemonic, as it is not useful for other products of polynomials.


`=18+6x+42x+14x^2 `

Now add the like terms (terms with the same variables to the same power) to get:

`=18+48x+14x^2 `

The solution is written as `14x^2+48x+18 ` ; this is in standard form. A polynomial is written in standard form if the terms are written so that the degree of the variable is in descending order. Thus we write the squared term first, then the linear term and finally the constant term.

Is `18+48x+14x^2 ` incorrect? No. The expressions `(3+7x)(6+2x),18+48x+14x^2,"and" 14x^2+48x+18 ` are all equivalent; that is they have the same value for the same inputs. However, the answer in standard form is the one most likely to be found in an answer key.

That is why the expression is "flipped", and there is nothing else you have to do.


`(3+7x)(6+2x)=14x^2+48x+18 `


** Be aware of the instructions. This problem probably had instructions to find the product, or write in standard form, or perhaps even simplify.

If your instructions say to evaluate, you will probably get a numerical answer, though sometimes you can get a variable expression.

If your instructions say to simplify, most of the time the answer is an expression.

Finally, if the instructions say to solve, the initial problem will have been an equation or an inequality, in which case the answer is a solution or solutions and will usually be a number or numbers.


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