Question

Simplify : (2x +3p)^3 + (2x -3p)^3

Answer 1

GIVEN :

Simplify : The expression is $(2x+3p)^3 + (2x-3p)^3$

TO FIND :

The simplified form for the given expression.

SOLUTION :

Given expression is $(2x+3p)^3 + (2x-3p)^3$

Now solving the expression as below :

$(2x+3p)^3 + (2x-3p)^3=(2x)^3+3(2x)^2(3p)+3(2x)(3p)^2+(3p)^3+(2x)^3-3(2x)^2(3p)+3(2x)(3p)^2-(3p)^3$

By using the Algebraic identities :

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

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

$=2^3x^3+3(2^2x^2)(3p)+3(2x)(3^2p^2)+3^3p^3+2^3x^3-3(2^2x^2)(3p)+3(2x)(3^2p^2)-3^3p^3$

By using the power rule exponent property :

$(ab)^m=a^mb^m$

$=8x^3+9p(4x^2)+6x(9p^2)+27p^3+8x^3-9p(4x^2)+6x(9p^2)-27p^3$

$=8x^3+6x(9p^2)+8x^3+6x(9p^2)$

$=8x^3+54xp^2+8x^3+54xp^$

By adding the like terms ,

$=16x^3+108xp^2$

$=4x(4x^2+27p^2)$

$(2x +3p)^3 + (2x -3p)^3=4x(4x^2+27p^2)$

∴ The simplified form for the given expression is $(2x +3p)^3 + (2x -3p)^3=4x(4x^2+27p^2)$