Help with simplification

**softwareguy** · March 20th 2010, 12:25 PM

Can someone please help me and explain each step to simplify the following:

$2t^3-2(t+h)^3$

I know the answer is:

$-6t^2h-6th^2-2h^3$

But I want to know how to get that simplification. I don't quite understand how to. Thanks.

**harish21** · March 20th 2010, 12:33 PM

Originally Posted by softwareguy

Can someone please help me and explain each step to simplify the following:

$2t^3-2(t+h)^3$

I know the answer is:

$-6t^2h-6th^2-2h^3$

But I want to know how to get that simplification. I don't quite understand how to. Thanks.

$(a+b)^3 = {a^3}+{b^3}+3{a^2}b+3a{b^2}$

so you have ,

$2{t^3} - 2 ({t^3}+{h^3}+3t{h^2}+3h{t^2})$

= $2{t^3} - 2{t^3}- 2{h^3}-6t{h^2}-6h{t^2}$

= $-2{h^3}-6t{h^2}-6h{t^2}$

= $-6t^2h-6th^2-2h^3$

**Anonymous1** · March 20th 2010, 12:55 PM

Note that,

$(a+b)^3 = (a+b)(a+b)(a+b)= (a^2 + 2ab + b^2)(a+b) = a^3 + 3a^2b + 3ab^2 + b^3$

**softwareguy** · March 21st 2010, 03:11 PM

Thank you so much guys!

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