Practice Page
Directions: Grab paper and pencil to show your work as you prepare these proofs.
1.
Prove, with justification, that this equation is an identity:
x2 + (a + b)x + ab = (x + a)(x + b).
splat1

 

 

2.
Determine if the following equation is an identity:
x6 + y6 = (x2 + y2)(x4 - x2y2 + y4).
splat2

 

 

3.
Serena presented the following solution to show that the following equation (where i is the imaginary unit) is NOT an identity.
x3 + 25x = x(x + 5i)(x - 5i)
STEP 1:
x3 + 25x  
= x(x2 + x5i - x5i - 25i2)
STEP 2:
  
= x(x2 + 25i2)
STEP 3:
  
= x3 + 25i2x
STEP 4:
  
= x3 - 25x      Not an identity!

Is her solution correct? If not, in which step did she make her error?

 

 

4.
Determine if the following equation is an identity:
m3 + n3 = (m + n)(m2 + mn + n2).
splat3



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