28) \( 16 x y-3 x-6 x^{2}+8 y \) 30) \( 14 v^{3}+10 v^{2}-7 v-5 \) 32) \( 28 p^{3}+21 p^{2}+20 p+15 \) 34) \( 42 r^{3}-21-49 r^{2}+18 r \) 36) \( -8 m+15 n-40+3 m n \) 30) \( 56 x-y+8 x y-7 \) 40) \( 24 x y+25 y^{2}-20 x-30 y^{3} \)

Factor the expression by following steps: - step0: Factor: \(28p^{3}+21p^{2}+20p+15\) - step1: Calculate: \(28p^{3}+20p+21p^{2}+15\) - step2: Rewrite the expression: \(4p\times 7p^{2}+4p\times 5+3\times 7p^{2}+3\times 5\) - step3: Factor the expression: \(4p\left(7p^{2}+5\right)+3\left(7p^{2}+5\right)\) - step4: Factor the expression: \(\left(4p+3\right)\left(7p^{2}+5\right)\) Factor the expression \( -8 m+15 n-40+3 m n \). Factor the expression by following steps: - step0: Factor: \(-8m+15n-40+3mn\) - step1: Calculate: \(3mn-8m+15n-40\) - step2: Rewrite the expression: \(m\times 3n-m\times 8+5\times 3n-5\times 8\) - step3: Factor the expression: \(m\left(3n-8\right)+5\left(3n-8\right)\) - step4: Factor the expression: \(\left(m+5\right)\left(3n-8\right)\) Factor the expression \( 24 x y+25 y^{2}-20 x-30 y^{3} \). Factor the expression by following steps: - step0: Factor: \(24xy+25y^{2}-20x-30y^{3}\) - step1: Calculate: \(-30y^{3}+25y^{2}+24xy-20x\) - step2: Rewrite the expression: \(-5y^{2}\times 6y+5y^{2}\times 5+4x\times 6y-4x\times 5\) - step3: Factor the expression: \(-5y^{2}\left(6y-5\right)+4x\left(6y-5\right)\) - step4: Factor the expression: \(\left(-5y^{2}+4x\right)\left(6y-5\right)\) - step5: Factor the expression: \(-\left(5y^{2}-4x\right)\left(6y-5\right)\) Factor the expression \( 56 x-y+8 x y-7 \). Factor the expression by following steps: - step0: Factor: \(56x-y+8xy-7\) - step1: Calculate: \(8xy+56x-y-7\) - step2: Rewrite the expression: \(8xy+8x\times 7-y-7\) - step3: Factor the expression: \(8x\left(y+7\right)-\left(y+7\right)\) - step4: Factor the expression: \(\left(8x-1\right)\left(y+7\right)\) Factor the expression \( 16 x y-3 x-6 x^{2}+8 y \). Factor the expression by following steps: - step0: Factor: \(16xy-3x-6x^{2}+8y\) - step1: Calculate: \(-6x^{2}-3x+16yx+8y\) - step2: Rewrite the expression: \(-3x\times 2x-3x+8y\times 2x+8y\) - step3: Factor the expression: \(-3x\left(2x+1\right)+8y\left(2x+1\right)\) - step4: Factor the expression: \(\left(-3x+8y\right)\left(2x+1\right)\) - step5: Factor the expression: \(-\left(3x-8y\right)\left(2x+1\right)\) Factor the expression \( 42 r^{3}-21-49 r^{2}+18 r \). Factor the expression by following steps: - step0: Factor: \(42r^{3}-21-49r^{2}+18r\) - step1: Calculate: \(42r^{3}+18r-49r^{2}-21\) - step2: Rewrite the expression: \(6r\times 7r^{2}+6r\times 3-7\times 7r^{2}-7\times 3\) - step3: Factor the expression: \(6r\left(7r^{2}+3\right)-7\left(7r^{2}+3\right)\) - step4: Factor the expression: \(\left(6r-7\right)\left(7r^{2}+3\right)\) Factor the expression \( 14 v^{3}+10 v^{2}-7 v-5 \). Factor the expression by following steps: - step0: Factor: \(14v^{3}+10v^{2}-7v-5\) - step1: Calculate: \(14v^{3}-7v+10v^{2}-5\) - step2: Rewrite the expression: \(7v\times 2v^{2}-7v+5\times 2v^{2}-5\) - step3: Factor the expression: \(7v\left(2v^{2}-1\right)+5\left(2v^{2}-1\right)\) - step4: Factor the expression: \(\left(7v+5\right)\left(2v^{2}-1\right)\) Here are the factored forms of the given expressions: 1. **For** \( 16 x y - 3 x - 6 x^{2} + 8 y \): \[ -(3x - 8y)(2x + 1) \] 2. **For** \( 14 v^{3} + 10 v^{2} - 7 v - 5 \): \[ (7v + 5)(2v^{2} - 1) \] 3. **For** \( 28 p^{3} + 21 p^{2} + 20 p + 15 \): \[ (4p + 3)(7p^{2} + 5) \] 4. **For** \( 42 r^{3} - 21 - 49 r^{2} + 18 r \): \[ (6r - 7)(7r^{2} + 3) \] 5. **For** \( -8 m + 15 n - 40 + 3 m n \): \[ (m + 5)(3n - 8) \] 6. **For** \( 56 x - y + 8 x y - 7 \): \[ (8x - 1)(y + 7) \] 7. **For** \( 24 x y + 25 y^{2} - 20 x - 30 y^{3} \): \[ -(5y^{2} - 4x)(6y - 5) \] If you need further assistance or explanations on any of these factorizations, feel free to ask!