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9 = 2(2x + 4)2, 9 = 2(4x2 + 16x + 16), 9 = 8x2 + 32x + 32 How did the 16x come about?

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2 Answers

9 = 2(2x + 4)2
  • n2 = (n)(n)
9 = 2(2x + 4)(2x + 4)
  • Using the distributive property of multiplication (a + b)(c + d) = ac + ad + bc + bd
  • We sometimes refer to this as FOIL (First, Outer, Inner, Last)
9 = 2[(2x)(2x) + (2x)(4) + (4)(2x) + (4)(4)]
9 = 2(4x2 + 8x + 8x + 16)
9 = 2(4x2 + 16x + 16)
  • Now distribute the 2
9 = 8x2 + 32x + 32
 
Did that help?
For 16x to be there the equation had to be 9 = 2(2x + 4)2
 
Now solving 9 = 2(2x + 4)2
 
9 = 2(2x + 4)(2x + 4)
 
opening the brackets
 
9 = 2(4x2 + 8x + 8x +16)
 
9 = 2(4x2 + 16x + 16) .................so 16x comes from 8x + 8x
 
further more opening the brackets 2 multiplies everything in it
 
9 = 8x+ 32x + 32
 
 
 

Comments

This leads me t another question, how did you get the 8x + 8x in the equation?
By multiplying (2x + 4) by (2x + 4) which is written as (2x + 4)(2x + 4) above in my answer.
when you do that you get
 
[ (2x * 2x) + (2x * 4) + (4 * 2x) + (4 * 4) ]
 
which gives 
 
[ (4x2) + (8x) + (8x) + (16) ]

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