3. \( -4 x\left(x^{2}+8\right) \) 4. \( \left(5-x^{2}+2\right)(-3) \) 5. \( 2 a^{2}\left(5 b^{2}+3 a b+6 a+1\right) \) 6. \( \left(3 x^{2}+6 x-5\right)(-3 x) \) 31

Simplify the expression by following steps: - step0: Rearrange the terms: \(\left(5-x^{2}+2\right)\left(-3\right)\) - step1: Add the numbers: \(\left(7-x^{2}\right)\left(-3\right)\) - step2: Multiply the terms: \(-3\left(7-x^{2}\right)\) - step3: Rearrange the terms: \(-21+3x^{2}\) Expand the expression \( -4 x\left(x^{2}+8\right) \) Simplify the expression by following steps: - step0: Multiply the terms: \(-4x\left(x^{2}+8\right)\) - step1: Apply the distributive property: \(-4x\times x^{2}-4x\times 8\) - step2: Multiply the terms: \(-4x^{3}-32x\) Expand the expression \( \left(3 x^{2}+6 x-5\right)(-3 x) \) Simplify the expression by following steps: - step0: Multiply the terms: \(\left(3x^{2}+6x-5\right)\left(-3x\right)\) - step1: Multiply the terms: \(-3x\left(3x^{2}+6x-5\right)\) - step2: Apply the distributive property: \(-3x\times 3x^{2}-3x\times 6x-\left(-3x\times 5\right)\) - step3: Multiply the terms: \(-9x^{3}-18x^{2}-\left(-15x\right)\) - step4: Remove the parentheses: \(-9x^{3}-18x^{2}+15x\) Expand the expression \( 2 a^{2}\left(5 b^{2}+3 a b+6 a+1\right) \) Simplify the expression by following steps: - step0: Calculate: \(2a^{2}\left(5b^{2}+3ab+6a+1\right)\) - step1: Rewrite the expression: \(2\left(5b^{2}+3ab+6a+1\right)a^{2}\) - step2: Rearrange the terms: \(\left(5b^{2}+3ab+6a+1\right)\times 2a^{2}\) - step3: Apply the distributive property: \(5b^{2}\times 2a^{2}+3ab\times 2a^{2}+6a\times 2a^{2}+1\times 2a^{2}\) - step4: Multiply the numbers: \(10b^{2}a^{2}+6a^{3}b+12a^{3}+2a^{2}\) Here are the expanded forms of the given expressions: 1. For \( -4 x\left(x^{2}+8\right) \): \[ -4 x^{3} - 32 x \] 2. For \( \left(5-x^{2}+2\right)(-3) \): \[ -21 + 3 x^{2} \] 3. For \( 2 a^{2}\left(5 b^{2}+3 a b+6 a+1\right) \): \[ 10 b^{2} a^{2} + 6 a^{3} b + 12 a^{3} + 2 a^{2} \] 4. For \( \left(3 x^{2}+6 x-5\right)(-3 x) \): \[ -9 x^{3} - 18 x^{2} + 15 x \] These expansions provide a clearer view of the polynomial expressions. If you have any further questions or need additional assistance, feel free to ask!