a. A = (a + b)3 + (a - b)3
A = (a + b + a - b)\(\left[\left(a+b\right)^2-\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)
A = 2a\(\left[\left(a^2+2ab+b^2\right)-\left(a^2-b^2\right)+\left(a^2-2ab+b^2\right)\right]\)
A = 2a(a2 + 2ab + b2 - a2 + b2 + a2 - 2ab + b2)
A = 2a(a2 + 3b2)
A = 2a3 + 3ab2
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a: \(A=\left(a+b\right)^3+\left(a-b\right)^3\)
\(=a^3+3a^2b+3ab^2+b^3+a^3-3a^2b+3ab^2-b^3\)
\(=2a^3+6ab^2\)
b: \(B=\left(x-y\right)^3+3xy\left(x+y\right)\)
\(=x^3-3x^2y+3xy^2-y^3+3x^2y+3xy^2\)
\(=x^3+6xy^2-y^3\)
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