Expand and simplify: \( \begin{array}{lll}\text { 1) } \\ \text { 3) } \\ \text { 3) } & (2 x+4)\left(x^{2}+2 x+3\right) & \text { (2) } \\ (x-1)\left(x^{2}-2 x+3\right) \\ \text { 5) } & (3 x-y)\left(2 x^{2}+4 x y-y^{2}\right) & \text { (4) } \\ & \text { (6) }(2 x-4)\left(x^{2}-3 x+1\right) \\ & & \end{array} \)

Simplify the expression by following steps: - step0: Multiply the terms: \(\left(x-1\right)\left(x^{2}-2x+3\right)\) - step1: Apply the distributive property: \(x\times x^{2}-x\times 2x+x\times 3-x^{2}-\left(-2x\right)-3\) - step2: Multiply the terms: \(x^{3}-2x^{2}+3x-x^{2}-\left(-2x\right)-3\) - step3: Remove the parentheses: \(x^{3}-2x^{2}+3x-x^{2}+2x-3\) - step4: Subtract the terms: \(x^{3}-3x^{2}+5x-3\) Expand the expression \( (2 x+4)(x^{2}+2 x+3) \) Simplify the expression by following steps: - step0: Multiply the terms: \(\left(2x+4\right)\left(x^{2}+2x+3\right)\) - step1: Apply the distributive property: \(2x\times x^{2}+2x\times 2x+2x\times 3+4x^{2}+4\times 2x+4\times 3\) - step2: Multiply the terms: \(2x^{3}+4x^{2}+6x+4x^{2}+8x+12\) - step3: Add the terms: \(2x^{3}+8x^{2}+14x+12\) Expand the expression \( (2 x-4)(x^{2}-3 x+1) \) Simplify the expression by following steps: - step0: Multiply the terms: \(\left(2x-4\right)\left(x^{2}-3x+1\right)\) - step1: Apply the distributive property: \(2x\times x^{2}-2x\times 3x+2x\times 1-4x^{2}-\left(-4\times 3x\right)-4\times 1\) - step2: Multiply the terms: \(2x^{3}-6x^{2}+2x-4x^{2}-\left(-12x\right)-4\) - step3: Remove the parentheses: \(2x^{3}-6x^{2}+2x-4x^{2}+12x-4\) - step4: Subtract the terms: \(2x^{3}-10x^{2}+14x-4\) Expand the expression \( (3 x-y)(2 x^{2}+4 x y-y^{2}) \) Simplify the expression by following steps: - step0: Multiply the terms: \(\left(3x-y\right)\left(2x^{2}+4xy-y^{2}\right)\) - step1: Apply the distributive property: \(3x\times 2x^{2}+3x\times 4xy-3xy^{2}-y\times 2x^{2}-y\times 4xy-\left(-y\times y^{2}\right)\) - step2: Multiply the terms: \(6x^{3}+12x^{2}y-3xy^{2}-2yx^{2}-4y^{2}x-\left(-y^{3}\right)\) - step3: Remove the parentheses: \(6x^{3}+12x^{2}y-3xy^{2}-2yx^{2}-4y^{2}x+y^{3}\) - step4: Subtract the terms: \(6x^{3}+10x^{2}y-7xy^{2}+y^{3}\) Here are the expanded and simplified results for each expression: 1) For \( (2x + 4)(x^2 + 2x + 3) \): \[ 2x^{3} + 8x^{2} + 14x + 12 \] 2) For \( (x - 1)(x^2 - 2x + 3) \): \[ x^{3} - 3x^{2} + 5x - 3 \] 3) For \( (3x - y)(2x^2 + 4xy - y^2) \): \[ 6x^{3} + 10x^{2}y - 7xy^{2} + y^{3} \] 4) For \( (2x - 4)(x^2 - 3x + 1) \): \[ 2x^{3} - 10x^{2} + 14x - 4 \] These results provide the expanded forms of the given expressions.