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\( (2x+5)^2 = 4x^2 + 20x + 25 \)
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The Deep Dive
To expand \( (2x + 5)^2 \), you can use the formula for the square of a binomial: \( (a + b)^2 = a^2 + 2ab + b^2 \). Here, \( a = 2x \) and \( b = 5 \). 1. First, square \( a \): \( (2x)^2 = 4x^2 \). 2. Then, square \( b \): \( 5^2 = 25 \). 3. Finally, calculate \( 2ab \): \( 2(2x)(5) = 20x \). Putting it all together, you get: \[ (2x + 5)^2 = 4x^2 + 20x + 25. \] So, the expanded form is \( 4x^2 + 20x + 25 \).
