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

Question

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

Answer 1

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?

Answer 2

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 = 8x² + 32x + 32