Expand Binomial Square: Expand the square of the binomial (2x-3)². (2x-3)² = (2x-3)(2x-3) = 2x(2x) + 2x(-3) + (-3)(2x) + (-3)(-3) = 4x² - 6x - 6x + 9 = 4x² - 12x + 9Distribute 4: Distribute 4 across the binomial (2x-3). 4(2x-3) = 4(2x) + 4(-3) = 8x - 12Combine and Subtract: Combine the expanded square from Step 1 with the result from Step 2 and subtract 5. 4x² - 12x + 9 + 8x - 12 - 5 = 4x² - 12x + 8x + 9 - 12 - 5 = 4x² - 4x + 9 - 12 - 5 = 4x² - 4x - 3

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$(2x-3)^{2}+4(2x-3)-5$

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Algebra 2

Add, subtract, multiply, and divide polynomials

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(2x-3)^{2}+4(2x-3)-5

Expand Binomial Square: Expand the square of the binomial $(2x-3)^2$ . $(2x-3)^2 = (2x-3)(2x-3) = 2x(2x) + 2x(-3) + (-3)(2x) + (-3)(-3) = 4x^2 - 6x - 6x + 9 = 4x^2 - 12x + 9$
Distribute $4$ : Distribute $4$ across the binomial $2x-3$ . $4(2x-3) = 4(2x) + 4(-3)$ $= 8x - 12$
Combine and Subtract: Combine the expanded square from Step $1$ with the result from Step $2$ and subtract $5$ . $4x^2 - 12x + 9 + 8x - 12 - 5$ $= 4x^2 - 12x + 8x + 9 - 12 - 5$ $= 4x^2 - 4x + 9 - 12 - 5$ $= 4x^2 - 4x - 3$