factorize \( m^{3}+n^{3} \) \( a^{12}-b^{6} \) \( 8 x^{3}-y^{9} \) \( x^{3}+8 y^{3} \)

Factor the expression \( m^{3}+n^{3} \). Factor the expression by following steps: - step0: Factor: \(m^{3}+n^{3}\) - step1: Factor the expression: \(\left(m+n\right)\left(m^{2}-mn+n^{2}\right)\) Factor the expression \( a^{12}-b^{6} \). Factor the expression by following steps: - step0: Factor: \(a^{12}-b^{6}\) - step1: Rewrite the expression: \(\left(a^{6}\right)^{2}-\left(b^{3}\right)^{2}\) - step2: Factor the expression: \(\left(a^{6}-b^{3}\right)\left(a^{6}+b^{3}\right)\) - step3: Factor the expression: \(\left(a^{2}-b\right)\left(a^{4}+a^{2}b+b^{2}\right)\left(a^{6}+b^{3}\right)\) - step4: Factor the expression: \(\left(a^{2}-b\right)\left(a^{4}+a^{2}b+b^{2}\right)\left(a^{2}+b\right)\left(a^{4}-a^{2}b+b^{2}\right)\) Factor the expression \( 8 x^{3}-y^{9} \). Factor the expression by following steps: - step0: Factor: \(8x^{3}-y^{9}\) - step1: Rewrite the expression: \(\left(2x\right)^{3}-y^{9}\) - step2: Factor the expression: \(\left(2x-y^{3}\right)\left(\left(2x\right)^{2}+2xy^{3}+y^{6}\right)\) - step3: Evaluate: \(\left(2x-y^{3}\right)\left(4x^{2}+2xy^{3}+y^{6}\right)\) Factor the expression \( x^{3}+8 y^{3} \). Factor the expression by following steps: - step0: Factor: \(x^{3}+8y^{3}\) - step1: Rewrite the expression: \(x^{3}+\left(2y\right)^{3}\) - step2: Factor the expression: \(\left(x+2y\right)\left(x^{2}-x\times 2y+\left(2y\right)^{2}\right)\) - step3: Calculate: \(\left(x+2y\right)\left(x^{2}-2xy+4y^{2}\right)\) The factorization of the given expressions is as follows: 1. \( m^{3}+n^{3} = (m+n)(m^{2}-mn+n^{2}) \) 2. \( a^{12}-b^{6} = (a^{2}-b)(a^{4}+a^{2}b+b^{2})(a^{2}+b)(a^{4}-a^{2}b+b^{2}) \) 3. \( 8 x^{3}-y^{9} = (2x-y^{3})(4x^{2}+2xy^{3}+y^{6}) \) 4. \( x^{3}+8 y^{3} = (x+2y)(x^{2}-2xy+4y^{2}) \)