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

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

### 2 Answers by Expert Tutors

Michael V. | Great Tutor in Multiple SubjectsGreat Tutor in Multiple Subjects
2
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

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Ebenezer O. | Aerospace Engr & Air Traffic Control Grad For General Ed. TutoringAerospace Engr & Air Traffic Control Gra...
4.6 4.6 (13 lesson ratings) (13)
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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