Help me thank you

Question

which expression can be equivalent to (w-6)(w+8) ? Explain please 

Answer 1

The easy-to-remember method of expanding this is called F-O-I-L,

                    for First  -  Outside  -  Inside  -  Last

The product of the First terms is w*w   or w²

Add the product of the Outside terms:    w*8

Add the product of the Inside terms:    -6*w

Finally, add the product of the Last Last terms:    -48

Adding them, that gives      w² + 2w - 48

 

Answer 2

There are a lot of expressions that can be considered "equivalent" to this one.  Any algebraic expression, in fact, can have many other expressions that are equivalent.

 

However, you use the work "which" in your question, which makes it sound like this may have been a multiple choice question and you need to pick the right one.

 

In any case, the usual thing to do when you have two binomial terms being multiplied is just to multiply them out.  That means multiply each value in the first term by each value in the second term and then add them together:

 

(w - 6) (w + 8)

 

w * w = w²

w  * 8 = 8w

(-6) * w = -6w

(-6) * 8 =-48

 

So that gives you w² + 8w - 6w - 48

 

You can combine the two terms with w to get w² + 2w - 48.  But you can't combine the w² term or the -48 term with anything, so you have to leave them as is.