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Multiply. \[ (5 x+4 y)(5 x-4 y) \] Simplify. your answer. \( \square \)

Ask by Wheeler Chavez. in the United States
Nov 09,2024

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\( 25x^{2}-16y^{2} \)

Solución

Calculate or simplify the expression \( (5*x+4*y)*(5*x-4*y) \). Simplify the expression by following steps: - step0: Solution: \(\left(5x+4y\right)\left(5x-4y\right)\) - step1: Simplify the product: \(\left(5x\right)^{2}-\left(4y\right)^{2}\) - step2: Evaluate the power: \(25x^{2}-16y^{2}\) The simplified result of multiplying \((5x+4y)(5x-4y)\) is \(25x^{2}-16y^{2}\).

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Mind Expander

To multiply the expression \( (5x + 4y)(5x - 4y) \), we can apply the difference of squares formula, which states that \( (a + b)(a - b) = a^2 - b^2 \). In this case: - \( a = 5x \) - \( b = 4y \) Using the formula, we have: \[ (5x + 4y)(5x - 4y) = (5x)^2 - (4y)^2 \] Now calculate each square: \[ (5x)^2 = 25x^2 \] \[ (4y)^2 = 16y^2 \] Putting it all together: \[ 25x^2 - 16y^2 \] So, the simplified answer is: \[ 25x^2 - 16y^2 \]

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