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5(x-2y)^(2)-(x-2y)

5(x2y)2(x2y) 5(x-2 y)^{2}-(x-2 y)

Full solution

Q. 5(x2y)2(x2y) 5(x-2 y)^{2}-(x-2 y)
  1. Write Expression: Write down the given expression.\newline5(x2y)2(x2y)5(x-2y)^{2}-(x-2y)
  2. Apply Distributive Property: Apply the distributive property to the first term by squaring x2yx-2y and multiplying by 55.5[(x2y)(x2y)](x2y)5[(x-2y)(x-2y)]-(x-2y)
  3. Expand Squared Term: Expand the squared term (x2y)(x2y)(x-2y)(x-2y).5[x22xy2xy+4y2](x2y)5[x^2 - 2xy - 2xy + 4y^2] - (x-2y)
  4. Combine Like Terms: Combine like terms within the expanded expression. 5[x24xy+4y2](x2y)5[x^2 - 4xy + 4y^2] - (x-2y)
  5. Distribute Across Terms: Distribute the 55 across the terms inside the brackets.5x220xy+20y2(x2y)5x^2 - 20xy + 20y^2 - (x-2y)
  6. Distribute Negative Sign: Distribute the negative sign across the terms in the second expression.\newline5x220xy+20y2x+2y5x^2 - 20xy + 20y^2 - x + 2y
  7. Combine Like Terms: Combine like terms.\newline(5x2x)+(20xy)+(20y2+2y)(5x^2 - x) + (-20xy) + (20y^2 + 2y)
  8. Simplify Expression: Simplify the expression by combining the coefficients of like terms.\newline(5x2x)20xy+(20y2+2y)(5x^2 - x) - 20xy + (20y^2 + 2y)
  9. Perform Subtraction: Perform the subtraction for the xx terms and addition for the yy terms.4x2x20xy+20y2+2y4x^2 - x - 20xy + 20y^2 + 2y

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