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Subtract 7x-5y+z from the product of 4 and (1)/(4)y-(1)/(2)x+3z

Subtract 7x−5y+z 7 x-5 y+z from the product of 44 and 14y−12x+3z \frac{1}{4} y-\frac{1}{2} x+3 z

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Simplify variable expressions involving like terms and the distributive propertyright chevron icon

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Q. Subtract 7x−5y+z 7 x-5 y+z from the product of 44 and 14y−12x+3z \frac{1}{4} y-\frac{1}{2} x+3 z
  1. Find Product Calculation: First, we need to find the product of 44 and the expression (14y−12x+3z)(\frac{1}{4}y - \frac{1}{2}x + 3z).\newlineCalculation: 4×(14y−12x+3z)4 \times (\frac{1}{4}y - \frac{1}{2}x + 3z)\newline= 4×(14y)−4×(12x)+4×3z4 \times (\frac{1}{4}y) - 4 \times (\frac{1}{2}x) + 4 \times 3z\newline= y−2x+12zy - 2x + 12z
  2. Subtract Expression Calculation: Now, we have to subtract the expression 7x−5y+z7x - 5y + z from the result we just found.\newlineCalculation: (y−2x+12z)−(7x−5y+z)(y - 2x + 12z) - (7x - 5y + z)\newline= y−2x+12z−7x+5y−zy - 2x + 12z - 7x + 5y - z
  3. Combine Like Terms Calculation: Next, we combine like terms to simplify the expression.\newlineCalculation: y−2x+12z−7x+5y−zy - 2x + 12z - 7x + 5y - z\newline= (y+5y)+(−2x−7x)+(12z−z)(y + 5y) + (-2x - 7x) + (12z - z)\newline= 6y−9x+11z6y - 9x + 11z

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