Question

(x+y)(x^2+y^2) -x^3-y^3

Answer 1

(x + y)(x² + y²) - x³ - y³ = x³ + xy² + x²y + y³ - x³ - y³ = xy² + x²y = xy(y + x)

Answer 2

=x3+xy2+x2y+y3-x3-y3=xy2+x2y

Answer 3

Let's expand the expression step by step:

(x+y)(x^2+y^2) = x(x^2+y^2) + y(x^2+y^2) // Distributive property = xx^2 + xy^2 + yx^2 + yy^2 // Distributive property = x^3 + xy^2 + xy^2 + y^3 // Simplify = x^3 + 2xy^2 + y^3

Now, we can subtract x^3 + y^3 from the above expression:

(x+y)(x^2+y^2) -x^3-y^3 = x^3 + 2xy^2 + y^3 - x^3 - y^3 // Substitute the expression we just derived = 2xy^2

Therefore, (x+y)(x^2+y^2) -x^3-y^3 simplifies to 2xy^2.