Hello,

I’m trying to work out {(x+h)^4 -x^4}/h

I would gratefully like the answer with explantion because I am having trouble working it out. Plus (X+h)^4, I need help working it out and somewhere I have seen a sort of general formulas for bracket sums with powers.

Thank you very much.

### 6 Answers

(x + h)⁴ = x⁴ + 4x³h + 6x²h² + 4xh³ + h⁴

the powers of the x decrease and the powers of the h increase

the coefficients come from pascals triangle

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

etc

These can also be found using combinations

nCr

(a + b)^n = ∑(r = 0 to n) nCr a^(n – r) b^r

X H 4

Memorize Pascal’s triangle it will help a lot, multiplying all the terms out takes far too long. I’ve included a link so you can see what I’m talking about.

Expanding (x+h)^4 results in

(x^4+4x^3h+6x^2h^2+4xh^3+h^4-x^4)/h

Simplifies to (4x^3h+6x^2h^2+4xh^3+h^4)/h after subtracting the x^4 term.

Dividing by h results in 4x^3+6x^2h+4xh^2+h^3.

This is your final answer.

(x+h)^4=[(x+h)^2]*[(x+h)^2]

This is the long way to do it, but it works with any number of terms inside the parentheses and any power.

The general formula for binomial powers comes from combinatorial calculus.

Look up Pascal’s triangle for a simple way to derive the coefficients.

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Hi, (x + 4)(x + 3) = x(x + 3) + 4(x + 3) = x² + 3x + 4x + 12 = x² + 7x + 12 <==ANSWER I hope that helps!! 🙂

try looking up the pascals triangle, it will help you a lot