Question

1. The area(in square centimeters) of a square coaster can be represented by

Answer 1

Answer: (d−4) 2

Explanation: Factoring  d2-8d+16

The first term is,  d2  its coefficient is  1 .

The middle term is,  -8d  its coefficient is  -8 .

The last term, "the constant", is  +16

Step-1 : Multiply the coefficient of the first term by the constant   1 • 16 = 16

Step-2 : Find two factors of  16  whose sum equals the coefficient of the middle term, which is   -8 .

     -16    +    -1    =    -17

     -8    +    -2    =    -10

     -4    +    -4    =    -8    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  -4

                    d2 - 4d - 4d - 16

Step-4 : Add up the first 2 terms, pulling out like factors :

                   d • (d-4)

             Add up the last 2 terms, pulling out common factors :

                   4 • (d-4)

Step-5 : Add up the four terms of step 4 :

                   (d-4)  •  (d-4)

            Which is the desired factorization

  Multiply  (d-4)  by  (d-4)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (d-4)  and the exponents are :

         1 , as  (d-4)  is the same number as  (d-4)1

and   1 , as  (d-4)  is the same number as  (d-4)1

The product is therefore,  (d-4)(1+1) = (d-4)2

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