Factories by splitting a middle term 2b square +32b+128
Answers
Answer:
Equation at the end of step 1
(2b2 - 32b) + 128
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
2b2 - 32b + 128 = 2 • (b2 - 16b + 64)
Trying to factor by splitting the middle term
3.2 Factoring b2 - 16b + 64
The first term is, b2 its coefficient is 1 .
The middle term is, -16b 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 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and -8
b2 - 8b - 8b - 64
Step-4 : Add up the first 2 terms, pulling out like factors :
b • (b-8)
Add up the last 2 terms, pulling out common factors :
8 • (b-8)
Step-5 : Add up the four terms of step 4 :
(b-8) • (b-8)
Which is the desired factorization
Answer:
2(b+8)(b+8)
Step-by-step explanation:
2b^2+32b+128
=2[(b)^2+2(b)(8)+(8)^2
=2[(b+8)^2]
=2(b+8)(b+8)