Answer:
(x+8)^2
Step-by-step explanation:
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Factoring x2+16x+64
The first term is, x2 its coefficient is 1 .
The middle term is, +16x its coefficient is 16 .
The last term, "the constant", is +64
Step-1 : Multiply the coefficient of the first term by the constant 1 • 64 = 64
Step-2 : Find two factors of 64 whose sum equals the coefficient of the middle term, which is 16 .
-64 + -1 = -65
-32 + -2 = -34
-16 + -4 = -20
-8 + -8 = -16
-4 + -16 = -20
-2 + -32 = -34
-1 + -64 = -65
1 + 64 = 65
2 + 32 = 34
4 + 16 = 20
8 + 8 = 16 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 8 and 8
x2 + 8x + 8x + 64
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+8)
Add up the last 2 terms, pulling out common factors :
8 • (x+8)
Step-5 : Add up the four terms of step 4 :
(x+8) • (x+8)
Which is the desired factorization
Multiply (x+8) by (x+8)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+8) and the exponents are :
1 , as (x+8) is the same number as (x+8)1
and 1 , as (x+8) is the same number as (x+8)1
The product is therefore, (x+8)(1+1) = (x+8)2
Final Result: (x + 8)2
