How do I solve (2x + h)^3??

(2x + h)^3
= (2x + h)(2x + h)(2x + h)
= (4x^2 + 2hx + 2hx + h^2)(2x + h)
= (4x^2 + 4hx + h^2)(2x + h)
= 8x^3 + 8hx^2 + 2h^2x + 4hx^2 + 4h^2x + h^3
= 8x^3 + 8hx^2 + 4hx^2 + 2h^2x + 4h^2x + h^3
= 8x^3 + 12hx^2 + 6h^2x + h^3

T (r+1) = (nCr) a^(n-r) b^(r)

(2x + h)^3
= 1(2x)^3 (h)^0 + 3(2x)^2 (h)^1 + 3(2x)^1(h)^2 + 1(2x)^0(h)^3
= 8x^3 + 6hx^2 + 6xh^2 + h^3

On your calculator (C is found by pressing nCr button)

[3C0 * (2x)³ * (h)°] + [3C1 * (2x)² * (h)¹] + [3C2 * (2x)¹ * (h)²] + [3C3 * (2x)° * (h)³]

Which gives you an answer of:

8x³ + 12x²h + 6xh² + h³

This is called the Binomial Expansion - there's plenty of stuff about it on the Internet

:)

What do you mean by " solve ? "
Solve applies to equations.

(2x + h) (2x + h)(2x + h)

(2x + h)(4x² + 4h x + h²)

8x³ + 8h x² + 2h² x
-------4h x² + 4h² x + h³

8x³ + 12h x² + 6h² x + h³

the formula is:
(a + b)^3 = a^3 + 3ba^2 + 3ab^2 + b^3

therefore:
(2x + h)^3 = (2x)^3 + 3(2x)h^2 + 3h(2x)^2 + h^3

= 8x^3 + 6xh^2 + 12hx^2 + h^3

...and that's as simplified as it will come. you cannot actually solve for x, unless there is an equals sign.

Hi,

(2x + h)³ =
(2x)³ + 3(2x)²(h) + 3(2x)(h)² + (h)³ =
8x³ + 12x²h + 6xh² + h³

I hope that helps!! :-)

(8x^3+12x^2 h + 6xh^2 + h^3)