Write Expression: Write down the given expression. 5(x-2y)^(2)-(x-2y)Apply Distributive Property: Apply the distributive property to the first term by squaring (x-2y) and multiplying by 5. 5[(x-2y)(x-2y)]-(x-2y)Expand Squared Term: Expand the squared term (x-2y)(x-2y). 5[x^2 - 2xy - 2xy + 4y^2] - (x-2y)Combine Like Terms: Combine like terms within the expanded expression. 5[x^2 - 4xy + 4y^2] - (x-2y)Distribute Across Terms: Distribute the 5 across the terms inside the brackets. 5x^2 - 20xy + 20y^2 - (x-2y)Distribute Negative Sign: Distribute the negative sign across the terms in the second expression. 5x^2 - 20xy + 20y^2 - x + 2yCombine Like Terms: Combine like terms. (5x^2 - x) + (-20xy) + (20y^2 + 2y)Simplify Expression: Simplify the expression by combining the coefficients of like terms. (5x^2 - x) - 20xy + (20y^2 + 2y)Perform Subtraction: Perform the subtraction for the x terms and addition for the y terms. 4x^2 - x - 20xy + 20y^2 + 2y

Algebra 1

Add and subtract polynomials

Full solution

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

Write Expression: Write down the given expression. $\newline$ $5(x-2y)^{2}-(x-2y)$
Apply Distributive Property: Apply the distributive property to the first term by squaring $x-2y$ and multiplying by $5$ . $5[(x-2y)(x-2y)]-(x-2y)$
Expand Squared Term: Expand the squared term $(x-2y)(x-2y)$ . $5[x^2 - 2xy - 2xy + 4y^2] - (x-2y)$
Combine Like Terms: Combine like terms within the expanded expression. $5[x^2 - 4xy + 4y^2] - (x-2y)$
Distribute Across Terms: Distribute the $5$ across the terms inside the brackets. $5x^2 - 20xy + 20y^2 - (x-2y)$
Distribute Negative Sign: Distribute the negative sign across the terms in the second expression. $\newline$ $5x^2 - 20xy + 20y^2 - x + 2y$
Combine Like Terms: Combine like terms. $\newline$ $(5x^2 - x) + (-20xy) + (20y^2 + 2y)$
Simplify Expression: Simplify the expression by combining the coefficients of like terms. $\newline$ $(5x^2 - x) - 20xy + (20y^2 + 2y)$
Perform Subtraction: Perform the subtraction for the $x$ terms and addition for the $y$ terms. $4x^2 - x - 20xy + 20y^2 + 2y$