Question

Algebraic expression and identity 1)simplify the following (3a+b)3 +(3a-b)3

Answer 1

Answer:

$(3a+b)^3+(3a-b)^3=54a^3+18ab^2$

Step-by-step explanation:

Given: $(3a+b)^3+(3a-b)^3$

Formula: $x^3+y^3=(x+y)(x^2-xy+y^2)$

$(x+y)^2=x^2+2xy+y^2$

$(x-y)^2=x^2-2xy+y^2$

$x\rightarrow 3a+b$

$y\rightarrow 3a-b$

$\Rightarrow (3a+b+3a-b)((3a+b)^2-(3a+b)(3a-b)+(3a-b)^2)$

$\Rightarrow (6a)(9a^2+b^2+6ab-9a^2+b^2+9a^2+b^2-6ab)$

$\Rightarrow (6a)(9a^2+3b^2)$

$\Rightarrow 54a^3+18ab^2$