3. Find the products. a) \( (a+b)\left(a^{2}-a b+b^{2}\right) \) b) \( (x-y)\left(x^{2}+x y+y^{2}\right) \)

To find the products, we can distribute each term in the first expression by the second expression. For the first expression: a) \( (a+b)(a^{2}-ab+b^{2}) \) expands to: - \( a \cdot a^{2} = a^{3} \) - \( a \cdot (-ab) = -a^{2}b \) - \( a \cdot b^{2} = ab^{2} \) - \( b \cdot a^{2} = a^{2}b \) - \( b \cdot (-ab) = -ab^{2} \) - \( b \cdot b^{2} = b^{3} \) Combining these gives us: \[ a^{3} + 0 + 0 + b^{3} = a^{3} + b^{3} \] For the second expression: b) \( (x-y)(x^{2}+xy+y^{2}) \) expands to: - \( x \cdot x^{2} = x^{3} \) - \( x \cdot xy = x^{2}y \) - \( x \cdot y^{2} = xy^{2} \) - \( -y \cdot x^{2} = -yx^{2} \) - \( -y \cdot xy = -y^{2}x \) - \( -y \cdot y^{2} = -y^{3} \) Combining these gives us: \[ x^{3} - y^{3} + 0 = x^{3} - y^{3} \] Thus, the final results are: a) \( a^{3} + b^{3} \) b) \( x^{3} - y^{3} \)