1, \(2xy^2z+7xy^2z+\left(-5xy^2z\right)\)
\(=\left(2+7-5\right)xy^2z\)
\(=4xy^2z\)
2, \(-\left(4uv^2-\dfrac{105}{2}uv^2+uv^2\right)+\left(-\dfrac{105}{2}uv^2+uv^2\right)\)
\(=-4uv^2+\dfrac{105}{2}uv^2-uv^2-\dfrac{105}{2}uv^2+uv^2\)
\(=-4uv^2+\left(\dfrac{105}{2}uv^2-\dfrac{105}{2}uv^2\right)+\left(uv^2-uv^2\right)\)
\(=-4uv^2\)
3, \(\left(3xy\right)^2-5x^2y^2+5xy^2\cdot\left(-2x\right)\)
\(=9x^2x^2-5x^2y^2+\left(5\cdot-2\right)\cdot\left(x\cdot x\right)\cdot y^2\)
\(=9x^2y^2-5x^2y^2-10x^2y^2\)
\(=\left(9-5-10\right)x^2y^2\)
\(=-6x^2y^2\)
4, \(5\cdot\left(2x\right)^2y^3+2xy\left(-3xy^2\right)+x^2y^3\)
\(=5\cdot4x^2y^3+\left(2\cdot-3\right)\cdot x^2y^3+x^2y^3\)
\(=20x^2y^3-6x^2y^3+x^2y^3\)
\(=\left(20-6+1\right)x^2y^3\)
\(=15x^2y^3\)
1) 2xy²z + 7xy²z + (-5xy²z)
= (2 + 7 - 5)xy²z
= 4xy²z
2) -(4uv² - 105/2 uv² + uv²) + (-105/2 uv²+ uv²)
= -4uv² + 105/2 uv² - uv² - 105/2 uv² + uv²
= -4uv² + (105/2 uv² - 105/2 uv²) + (-uv² + uv²)
= = -4uv²
3) (3xy)² - 5x²y² + 5xy².(-2x)
= 9x²y² - 5x²y² + 10x²y²
= (9 - 5 + 10)x²y²
= 14x²y²
4) 5(-2x)²y³ + 2xy(-3xy²) + x²y³
= 20x²y³ - 6x²y³ + x²y³
= (20 - 6 + 1)x²y³
= 15x²y³
