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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