(2+h)3rd power (or cubed)?

Question

g=(2+h) question is (2+h) cubed; need worked out problem, my book says answer is 8+12h+6h(squared)+h(cubed) I don't get it

(2+h)^3 Need written expanation for answer

Answer 1

(2+h)^3
= (2+h)(2+h)(2+h)

First, calculate (2+h)(2+h)
= 2(2) + 2(h) + 2(h) + h^2

Combine like terms:
= 4 + 4h + h^2

Now you have:
(2+h)(4 + 4h + h^2)

Now you need to multiply each term again:
(2+h)(4 + 4h + h^2)
2(4) + 2(4h) + 2(h^2) + h(4) + h(4h) + h(h^2)
= 8 + 8h + 2h^2 + 4h + 4h^2 + h^3

Now combine like terms:
= 8 + 12h + 6h^2 + h^3

Answer 2

(2 + h)^3 {can also be written as...}
= (2 + h)*(2 + h)*(2 + h) {First do the calculation of (2 + h)*(2 + h)}
= (2 + h)*(2*2 + 2*h + h*2 + h*h) {Now, simplify the expansion}
= (2 + h)*(4 + 4h + h^2) {Now, multiply the obtained expression by (2 + h)}
= 2*4 + 2*4h + 2*h^2 + 4*h + 4h*h + h*h^2 {Simplify your obtained expression}
= 8 + 8h + 2h^2 + 4h + 4h^2 + h^3
= h^3 + 6h^2 + 12h +8 {This is the answer you want}


Hope this helps!

Answer 3

Solve (2+h)^3 (without plugging into a formula):

(2+h)^3 = (2+h)(2+h)(2+h)

(2+h)(2+h) = (4 + 2h + 2h + h^2)
Simplify (combine terms/rearrange from highest power to lowest)
(2+h)(2+h) = (h2 + 4h + 4)

(2+h)(2+h)(2+h) = (h^2 + 4h + 4)(2 + h)
= (2h^2 + h^3 + 8h + 4h^2 + 8 + 4h)
Simplify (combine terms/rearrange from highest power to lowest)
(2+h)^3 = (h^3 + 6h^2 + 12h + 8)_______****ANSWER****

Answer 4

theoretically there exits a formula

(a+b)^3 = a^3 +3ba^2+3a b^2+b^3

which gives here (2+h)^3 = 8 +12h + 6h^2 +h^3

we will check step by step

(2+h) ^3 = (2+h)^2*(2+h)

(2+h)^2* = 4+4h +h^2

and (4+4h +h^2) (2+h)= 8+8h+2h^2+4h+4h^2+h^3

Answer 5

(2+h)^3
=2^2+3.4.h+3.2.h^2+h^3.......
this is a formula a^3+3a^2b+3ab^2+B^3
=4+12h+6h^2+h^3...ur answer

or u can do it like (2+h)^2 X(2+h)
=(4+4h+h^2)(2+h)
=8+8h+2h^2+8h+4h^2+h^3
8+12h+6h^2+h^3..ur answer again.

Answer 6

(2+h)^3=?
coefficients comes from pascal triangle
1
3
3
1

remember
(a+b)^3=a^3+3a^2b+3a b^2+b^3
here a=2
b=h

then
(2+h)^3
=2^3+3*2^2*h+3*2*h^2+h^3
=8+12h+6h^2+h^3

Answer 7

(2+h)3=(2+h)(2+h)(2+h)
=(h2+4h+4)(2+h)
=h3+6h2+12h+8

Answer 8

it can be seperated in two.. (2+h)^2 (2+h)... square (2+h) , it will giv u h^2+4h+4. then multiplt it by (2+h)....

thats the answer... solve it..

Answer 9

squared = ^2
x(quared) = x^2
cubed=^3
x(cubed) = x^3