1. \( \sqrt{5 a-2 b} \), cuando \( a=10 \) y \( b=2 \). 2. \( (x+2 y)^{2} \), cuando \( x=4, y=-1 \) y \( z=3 \). 3. \( \sqrt{(x+2 y)(x-2 y)} \), si \( x=10 \) y \( y=2 \). 4. \( 3 \pi+5 a \div 2-\{2(a+b)-3\}-3 \pi \), cuando \( a=10 \mathrm{y} b=2 \). 5. \( (a+2 b) \div c \), suponiendo que \( a=1, b=2 \mathrm{y} c=3 \). 6. \( (a+p \div q)(3 q \div(p+q)) \), si \( p=6 \mathrm{y} q=3 \). 7. \( 2 x^{3}-5 x^{2}+4 x-6 \), para \( x=-2 \) 8. \( (x+z-y)(x-z+y) \), con \( x=y=4 \mathrm{y} z=-4 \) 9. \( -(-x)-x-(x-x)-3 \) para \( x=3 \) 10. \( 4 a-a^{2}+5 b-2 \) si \( a=1 \) y \( b=-3 \)

Evaluate the expression by following steps: - step0: Evaluate: \(\left(a+2b\right)\div c\) - step1: Substitute: \(\left(1+2\times 2\right)\div 3\) - step2: Multiply the numbers: \(\left(1+4\right)\div 3\) - step3: Add the numbers: \(5\div 3\) - step4: Rewrite the expression: \(\frac{5}{3}\) Substitute \( a=1,b=-3 \) into the expression \( 4 a-a^{2}+5 b-2 \). Evaluate the expression by following steps: - step0: Evaluate: \(4a-a^{2}+5b-2\) - step1: Substitute: \(4\times 1-1^{2}+5\left(-3\right)-2\) - step2: Evaluate the power: \(4\times 1-1+5\left(-3\right)-2\) - step3: Multiply: \(4-1+5\left(-3\right)-2\) - step4: Multiply the numbers: \(4-1-15-2\) - step5: Subtract the numbers: \(-14\) Substitute \( x=-2 \) into the expression \( 2 x^{3}-5 x^{2}+4 x-6 \). Evaluate the expression by following steps: - step0: Evaluate: \(2x^{3}-5x^{2}+4x-6\) - step1: Substitute: \(2\left(-2\right)^{3}-5\left(-2\right)^{2}+4\left(-2\right)-6\) - step2: Multiply the terms: \(-2^{4}-5\left(-2\right)^{2}+4\left(-2\right)-6\) - step3: Multiply the terms: \(-2^{4}-20+4\left(-2\right)-6\) - step4: Multiply the numbers: \(-2^{4}-20-8-6\) - step5: Evaluate the power: \(-16-20-8-6\) - step6: Subtract the numbers: \(-50\) Substitute \( x=4,y=-1 \) into the expression \( (x+2 y)^{2} \). Evaluate the expression by following steps: - step0: Evaluate: \(\left(x+2y\right)^{2}\) - step1: Substitute: \(\left(4+2\left(-1\right)\right)^{2}\) - step2: Simplify: \(\left(4-2\right)^{2}\) - step3: Subtract the numbers: \(2^{2}\) - step4: Evaluate the power: \(4\) Substitute \( a=10,b=2 \) into the expression \( \sqrt{5 a-2 b} \). Evaluate the expression by following steps: - step0: Evaluate: \(\sqrt{5a-2b}\) - step1: Substitute: \(\sqrt{5\times 10-2\times 2}\) - step2: Multiply the numbers: \(\sqrt{50-2\times 2}\) - step3: Multiply the numbers: \(\sqrt{50-4}\) - step4: Subtract the numbers: \(\sqrt{46}\) Substitute \( x=10,y=2 \) into the expression \( \sqrt{(x+2 y)(x-2 y)} \). Evaluate the expression by following steps: - step0: Evaluate: \(\sqrt{\left(x+2y\right)\left(x-2y\right)}\) - step1: Substitute: \(\sqrt{\left(10+2\times 2\right)\left(10-2\times 2\right)}\) - step2: Multiply the numbers: \(\sqrt{\left(10+4\right)\left(10-2\times 2\right)}\) - step3: Add the numbers: \(\sqrt{14\left(10-2\times 2\right)}\) - step4: Multiply the numbers: \(\sqrt{14\left(10-4\right)}\) - step5: Subtract the numbers: \(\sqrt{14\times 6}\) - step6: Multiply the numbers: \(\sqrt{84}\) - step7: Write as a product: \(\sqrt{4\times 21}\) - step8: Write in exponential form: \(\sqrt{2^{2}\times 21}\) - step9: Use the properties of radicals: \(\sqrt{2^{2}}\times \sqrt{21}\) - step10: Simplify the root: \(2\sqrt{21}\) Substitute \( a=10,b=2 \) into the expression \( 3 \pi+5 a \div 2-\{2(a+b)-3\}-3 \pi \). Evaluate the expression by following steps: - step0: Evaluate: \(3\pi +5a\div 2-\left(2\left(a+b\right)-3\right)-3\pi \) - step1: Substitute: \(3\pi +5\times 10\div 2-\left(2\left(10+2\right)-3\right)-3\pi \) - step2: Add the numbers: \(3\pi +5\times 10\div 2-\left(2\times 12-3\right)-3\pi \) - step3: Multiply the numbers: \(3\pi +5\times 10\div 2-\left(24-3\right)-3\pi \) - step4: Multiply the numbers: \(3\pi +50\div 2-\left(24-3\right)-3\pi \) - step5: Subtract the numbers: \(3\pi +50\div 2-21-3\pi \) - step6: Divide the numbers: \(3\pi +25-21-3\pi \) - step7: Remove the opposites: \(4\) Substitute \( p=6,q=3 \) into the expression \( (a+p \div q)(3 q \div(p+q)) \). Evaluate the expression by following steps: - step0: Evaluate: \(\left(a+p\div q\right)\left(3q\div \left(p+q\right)\right)\) - step1: Substitute: \(\left(a+6\div 3\right)\left(3\times 3\div \left(6+3\right)\right)\) - step2: Divide the numbers: \(\left(a+2\right)\left(3\times 3\div \left(6+3\right)\right)\) - step3: Add the numbers: \(\left(a+2\right)\left(3\times 3\div 9\right)\) - step4: Multiply the numbers: \(\left(a+2\right)\left(9\div 9\right)\) - step5: Divide the numbers: \(\left(a+2\right)\times 1\) - step6: Multiply: \(a+2\) Substitute \( x=4,y=4,z=-4 \) into the expression \( (x+z-y)(x-z+y) \). Evaluate the expression by following steps: - step0: Evaluate: \(\left(x+z-y\right)\left(x-z+y\right)\) - step1: Substitute: \(\left(4-4-4\right)\left(4-\left(-4\right)+4\right)\) - step2: Subtract the numbers: \(\left(-4\right)\left(4-\left(-4\right)+4\right)\) - step3: Remove the parentheses: \(-4\left(4-\left(-4\right)+4\right)\) - step4: Calculate: \(-4\times 12\) - step5: Multiply the numbers: \(-48\) Substitute \( x=3 \) into the expression \( -(-x)-x-(x-x)-3 \). Evaluate the expression by following steps: - step0: Evaluate: \(-\left(-x\right)-x-\left(x-x\right)-3\) - step1: Substitute: \(-\left(-3\right)-3-\left(3-3\right)-3\) - step2: Subtract the terms: \(-\left(-3\right)-3-0-3\) - step3: Remove 0: \(-\left(-3\right)-3-3\) - step4: Simplify: \(3-3-3\) - step5: Subtract the numbers: \(-3\) Aquí están los resultados de las expresiones evaluadas: 1. Para \( \sqrt{5 a-2 b} \) cuando \( a=10 \) y \( b=2 \): \[ \sqrt{46} \] 2. Para \( (x+2 y)^{2} \) cuando \( x=4 \) y \( y=-1 \): \[ 4 \] 3. Para \( \sqrt{(x+2 y)(x-2 y)} \) si \( x=10 \) y \( y=2 \): \[ 2\sqrt{21} \] 4. Para \( 3 \pi+5 a \div 2-\{2(a+b)-3\}-3 \pi \) cuando \( a=10 \) y \( b=2 \): \[ 4 \] 5. Para \( (a+2 b) \div c \) suponiendo que \( a=1, b=2 \) y \( c=3 \): \[ \frac{5}{3} \quad \text{o} \quad 1\frac{2}{3} \quad \text{o} \quad 1.6\overline{6} \] 6. Para \( (a+p \div q)(3 q \div(p+q)) \) si \( p=6 \) y \( q=3 \): \[ a+2 \] 7. Para \( 2 x^{3}-5 x^{2}+4 x-6 \) para \( x=-2 \): \[ -50 \] 8. Para \( (x+z-y)(x-z+y) \) con \( x=y=4 \) y \( z=-4 \): \[ -48 \] 9. Para \( -(-x)-x-(x-x)-3 \) para \( x=3 \): \[ -3 \] 10. Para \( 4 a-a^{2}+5 b-2 \) si \( a=1 \) y \( b=-3 \): \[ -14 \] Si necesitas más ayuda o aclaraciones, no dudes en preguntar.