Answer:
[tex](3a+b)^3+(3a-b)^3=54a^3+18ab^2[/tex]
Step-by-step explanation:
Given: [tex](3a+b)^3+(3a-b)^3[/tex]
Formula: [tex]x^3+y^3=(x+y)(x^2-xy+y^2)[/tex]
[tex](x+y)^2=x^2+2xy+y^2[/tex]
[tex](x-y)^2=x^2-2xy+y^2[/tex]
[tex]x\rightarrow 3a+b[/tex]
[tex]y\rightarrow 3a-b[/tex]
[tex]\Rightarrow (3a+b+3a-b)((3a+b)^2-(3a+b)(3a-b)+(3a-b)^2)[/tex]
[tex]\Rightarrow (6a)(9a^2+b^2+6ab-9a^2+b^2+9a^2+b^2-6ab)[/tex]
[tex]\Rightarrow (6a)(9a^2+3b^2)[/tex]
[tex]\Rightarrow 54a^3+18ab^2[/tex]
