Question

Can you pls solve???? thank you

Answer 1

`\boxed{\mbox{\large 4x\:+\:2h\:-\:6}}`

Explanation:

We ae given

Looking at individual terms,

• Expand the term
  
  `(x + h)^2 = x^2 + 2xh + h^2\\\\2(x+h)^2 = 2( x^2 + 2xh + h^2)\\\\=2x^2 +4xh +2h^2`
• Expand the term 6(x + h)
  = 6x + 6h
  
• Therefore
  
  `f(x + h) = 2x^2+4xh+2h^2-6x-6h-4`
  
• 
  `f(x+h) - f(x)`
  
  `= 2x^2+4xh+2h^2-6x-6h-4\:-\left(2x^2-6x\:-\:4\right)\\\\= 2x^2+4xh+2h^2-6x-6h-4\;-2x^2+ 6x + 4\\\\`
  
• Group like terms:
  
  `= 2x^2-2x^2+4xh-6x+6x+2h^2-6h-4+4`
  =
  `4xh+2h^2-6h`
  
• Therefore
  
  
  `(f(x+h) - f(x))/(h)\\\\= (4xh+2h^2-6h)/(h)\\\\= 4x + 2h - 6`