How do you simplify this?

Question

[4(x+h)^2 + 3 (x+h) + 4] - (4x^2+3x+4)

I think it's supposed to be (8x+3)h+4h^2
...but I dont get how. Plz show me. thnx anyone?

Answer 1

Expand the binomial squares

4(x^2 + 2xh + h^2) + 3(x + h) + 4 - (4x^2 + 3x + 4)

Distribute

4x^2 + 8xh + 4h^2 + 3x + 3h + 4 - 4x^2 - 3x - 4

Combine like terms

8xh + 4h^2 + 3h

Re-arrange and factor to get your result

8xh + 3h + 4h^2
(8x + 3)h + 4h^2

Answer 2

It's easy. U can recognise (well, actually i'm not native speaker :D) that the numbers are the same and the ... srtuctures are somehow similar, so u just need to expand:
4 x^2 + 8 x h + 4 h^2 + 3 x + 3 h + 4 - 4 x^2 - 3 x -4
then it'll be:
8 x h + 3 h + 4 h^2 = the answer u think it's supposed to be.
:D

Answer 3

[4(x+ h)^2 + 3(x + h) + 4] - (4x^2 + 3x + 4)

= [4(x +h)(x +h) + 3(x + h) + 4] - (4x^2 + 3x + 4)

= [4(x^2 + xh + xh + h^2) + 3(x + h) + 4] - (4x^2 + 3x +4)

= 4x^2 + 4xh + 4xh + 4h^2 + 3x + 3h + 4 - 4x^2 - 3x - 4

= 8xh +4h^2 + 3h or (8x + 3)h + 4h^2

=h(8x + 4h + 3)

Answer 4

4(x + h)² :--------4x² + 8 h x + 4 h²
3 (x + h) + 4 = ------------------------3x + 3h + 4
-(4x² + 3x + 4)= - 4x²--------------- -3x------- - 4
Adding gives:-
8 h x + 4h² + 3h = h.(8x + 3) + 4 h²--------+++
This agrees with your answer.
As a matter of interest, this equation is used to differentiate f(x) from 1st principles , where:-
f(x) = 4x² + 3x + 4
f ` (x) = 8x + 3
This answer would be obtained by dividing +++ above by h and then let h-->0

Answer 5

[4(x+h)^2 + 3 (x+h) + 4] - (4x^2+3x+4)
=4(x+h)^2 - 4x^2 + 3 (x+h) - 3x + 4 - 4
=4[(x+h)^2 - x^2] +3(x+h-x)
=4[(x+h+x)(x+h-x)] + 3h ------- (a^2 - b^2) = (a+b)(a-b)
=4[(2x+h)h] + 3h
=8xh + 4h^2 + 3h
=(8x+3)h + h^2

Answer 6

4585-*9+5926985-1+961
9651-+9652+956--+94650+25+3+45