Question

what is the factored form of the expression?
1. w^2 + 12w + 36
2. t^2 + 10^2 +25
3. t^2 - 81
@kewlgeek555

Answer 1

1. (w+6)2
2. t2+125
3. t2+81

Answer 2

Oops - I got the third one wrong.

Answer 3

3. The polynomial is not factorable with real numbers.

Answer 4

The second one isn't a option on the assingment

Answer 5

Actually, @kewlgeek555 's answers are wrong on 2 and 3. And you shouldn't be giving answers, anyway.

Answer 6

On #2, shouldn't the middle term be 10t, not 10^2?

The 3rd one factors as a difference of squares.

Answer 7

\(\Large a^2-b^2=(a+b)(a-b)\)

Apply that in the 3rd one.

Answer 8

Ohh , yes thanks , i need help understanding

Answer 9

There are some "special products" that you can "reverse" for factoring. Remember, factoring a polynomial of this type is really just "undoing" the FOIL that it takes to get it. I gave you one rule above already:

\(\Large a^2-b^2=(a+b)(a-b)\)

You probably remember learning this, in the "reverse" direction, when you learned to MULTIPLY binomials.

Another one you probably learned is this:
\(\Large a^2+2ab +b^2=(a+b)^2\)

Again, in the REVERSE direction, this is the rule for squaring a binomial that is a sum. But you can UNDO that multiplication with factoring, with the trinomial has the form that is on the right.

Of course, if you forget the special rule, you can always do it with "trial and error" just by writing the same factor twice:
\(\Large a^2+2ab +b^2=(a+b)(a+b)\)

Answer 10

Thanks :)

Answer 11

youre welcome :)